Change detection (CD) in remote sensing images is an important problem requiring the analysis of high-dimensional data such as radar, multispectral, and hyperspectral images. Solutions for radar and multispectral data are available in the literature. However, the use of hyperspectral images is still an area of improvement, not only because the existing methods were designed to handle a reduced number of spectral bands but also because they do not fully exploit the rich spectral information available for CD. Additionally to the use of hyperspectral data, the interest in multimodal CD is that different sensors, such as optical and synthetic aperture radar (SAR), can contribute with essential features improving the generation of high-quality change maps. This paper addresses the multimodal CD problem using hyperspectral and optical/SAR images or pairs of hyperspectral images using a multivariate manifold estimation model based on spectral unmixing. The estimated abundance maps associated with hyperspectral images are used as inputs to the CD strategy, instead of the original hyperspectral data enabling significant dimensionality reduction. Several simulations demonstrate the effectiveness of the proposed approach, achieving, for instance, overall accuracy values above 91%, AUC values up to 0.95, and consistently higher recall compared to competing methods. These results highlight the strong performance of the proposed method while preserving its flexibility to handle any combination of radar, multispectral, and hyperspectral images. • Spectral information can play a fundamental role for change detection. • Proposes a multivariate manifold estimation model based on spectral unmixing. • A model that adapts and accommodates various multimodal sensor combinations.

The estimation of high resolution spectrometer Instrument Spectral Response Functions (ISRFs) is crucial because an imperfect knowledge of these functions can induce errors in the measurements. The state-of-the-art for this problem currently relies on the use of parametric models, which frequently lack flexibility to accurately model real-world ISRFs. To address this limitation, this paper proposes and investigates the use of sparse representations for modeling and estimating ISRFs, where the ISRFs are decomposed in a fixed dictionary of atoms. To estimate the sparse coefficient vector, a novel sparsity inducing regularization of the problem based on quadratic envelopes is studied and compared to the classical LASSO estimator and to a greedy method based on the Orthogonal Matching Pursuit (OMP) algorithm. Results for simulated ISRFs from the MicroCarb mission indicate that the proposed spectral representations yield excellent ISRF estimates, and that the use of quadratic envelopes can yield significantly better precision than competing methods.

Multifractal analysis (MFA) provides a framework for the global characterization of image textures by describing the spatial fluctuations of their local regularity based on the multifractal spectrum. Several works have shown the interest of using MFA for the description of homogeneous textures in images. Nevertheless, natural images can be composed of several textures and, in turn, multifractal properties associated with those textures. This paper introduces an unsupervised Bayesian multifractal segmentation method to model and segment multifractal textures by jointly estimating the multifractal parameters and labels on images, at the pixel-level. For this, a computationally and statistically efficient multifractal parameter estimation model for wavelet leaders is firstly developed, defining different multifractality parameters for different regions of an image. Then, a multiscale Potts Markov random field is introduced as a prior to model the inherent spatial and scale correlations (referred to as cross-scale correlations) between the labels of the wavelet leaders. A Gibbs sampling methodology is finally used to draw samples from the posterior distribution of the unknown model parameters. Numerical experiments are conducted on synthetic multifractal images to evaluate the performance of the proposed segmentation approach. The proposed method achieves superior performance compared to traditional unsupervised segmentation techniques as well as modern deep learning-based approaches, showing its effectiveness for multifractal image segmentation.

Understanding greenhouse gas fluxes at the Earth’s surface is becoming crucial in the context of climate change. The aim of the CNES/UKSA MicroCarb mission is therefore to map, on a planetary scale, the sources and sinks of carbon, the main greenhouse gas in the atmosphere. To do this, a spectrometer will be sent in space to acquire spectra in 4 narrow bands around wavelengths associated with O2and CO2. However, measurement errors can occur due to the instrument used, and induce errors in the resulting trace gas concentrations. It is therefore crucial to estimate the spectral response of the instrument as accurately as possible. This paper investigates a new estimation method for this spectral response that uses a sparse representation in a dictionary of appropriate basis functions. This sparse representation is performed using the LASSO and Orthogonal Matching Pursuit (OMP) algorithms. Simulations conducted on data mimicking observations resulting from the MicroCarb instrument allow the performance of this method to be appreciated.

This paper derives and studies Bayesian Cramér-Rao lower bounds for the mean squared error of covariance matrices that are structured as weighted sums of symmetric positive definite matrices associated with a circularly-symmetric Gaussian statistical model. This model naturally appears in a number of important applications, including multivariate multifractal analysis and vector-valued additive Gaussian processes. As an intermediary result, we derive a novel expression for the expectation of compositions of Wishart random matrices. We provide extensive numerical simulation results for analyzing the derived bounds and their properties, and illustrate their use for the multifractal analysis of bivariate time series.

Multifractal analysis provides a global description for the spatial fluctuations of the strengths of the pointwise regularity of image amplitudes. A global image characterization leads to robust estimation, but is blind to and corrupted by small regions in the image whose multifractality differs from that of the rest of the image. Prior detection of such zones with anomalous multifractality is thus crucial for relevant analysis, and their delineation of central interest in applications, yet has never been achieved so far. The goal of this work is to devise and study such a multifractal anomaly detection scheme. Our approach combines three original key ingredients: i) a recently proposed generic model for the statistics of the multiresolution coefficients used in multifractal estimation (wavelet leaders), ii) an original surrogate data generation procedure for simulating a hypothesized global multifractality and iii) a combination of multiple hypothesis tests to achieve pixel-wise detection. Numerical simulations using synthetic multifractal images show that our procedure is operational and leads to good multifractal anomaly detection results for a range of target sizes and parameter values of practical relevance.

Most modern congestion control algorithms, that aim to optimize delay and throughput, exploit more metrics than the sole packet loss congestion information. These additional metrics are mostly based on the round trip time evolution and allow congestion controls to reach better performance, in particular on wireless and cellular links as demonstrated by Copa, BBR, or REMY. Basically, these metrics allow congestion control to estimate the queuing level of the path and its evolution, to assess the presence of congestion. Actually, a good estimation of this level obviously prevents congestion losses, but also allows assessing a ratio of error link losses among the whole observed losses. The consistency and accuracy of these metrics are key to good congestion control performance, and this explains, for instance, the good performance of Copa currently in production at Facebook. However, these metrics remain challenging and the quest of an accurate and practical estimation seems complex. This paper investigates how a novel deep learning algorithm, known as Attention, can help in assessing queuing evolution and status on an end-to-end path. Among others, we focus on the evolution of the total time spent by packets in the buffers, which is the key metric of Copa. The results unequivocally demonstrate a better accuracy of this metric used by Copa.

Monitoring agriculture from satellite remote sensing data, such as multispectral images, has become a powerful tool since it has demonstrated a great potential for providing timely and accurate knowledge of crops. Detecting anomalies in time series of multispectral remote sensing images for crop monitoring is generally performed using a large sample of historical data at a pixel level. Conversely, this article presents a framework for anomaly detection (AD), localization, and classification that exploits the temporal information contained in a given season at a parcel level to detect and localize outliers using hidden Markov models (HMMs). Specifically, the AD part is based on the learning of HMM parameters associated with unlabeled normal data that are used in a second step to detect abnormal crop parcels referred to as anomalies. The learned HMM can also be used in time segments to temporally localize the anomalies affecting the crop parcels. The detected and localized anomalies are finally classified using a supervised classifier, e.g., based on support vector machines. The proposed framework is applicable to images partially covered by clouds and can handle a set of crop parcels acquired in the same season bypassing problems due to crop rotations. Numerical experiments are conducted on synthetic and real data, where the real data correspond to vegetation indices extracted from several multitemporal Sentinel-2 images of rapeseed crops. The proposed approach is compared to standard AD methods yielding better detection rates with the advantage of allowing anomalies to be localized and characterized.

The first part of this paper presents some works conducted with Jose Bioucas Dias for fusing high spectral resolution images (such as hyperspectral images) and high spatial resolution images (such as panchromatic or multispectral images) in order to build images with improved spectral and spatial resolutions. These works are related to Bayesian fusion strategies exploiting prior information about the target image to be recovered constructed by dictionary learning. Interestingly, these Bayesian image fusion methods can be adapted with limited changes to motion estimation in pairs or sequences of images. The second part of this paper explains how the work of Jose Bioucas Dias has been a source of inspiration for developing new Bayesian motion estimation methods for ultrasound images.

This letter studies a new expectation maximization (EM) algorithm to solve the problem of circle, sphere and more generally hypersphere fitting. This algorithm relies on the introduction of random latent vectors having a priori independent von Mises-Fisher distributions defined on the hypersphere. This statistical model leads to a complete data likelihood whose expected value, conditioned on the observed data, has a Von Mises-Fisher distribution. As a result, the inference problem can be solved with a simple EM algorithm. The performance of the resulting hypersphere fitting algorithm is evaluated for circle and sphere fitting.

This paper introduces a convolutional sparse model for anomaly detection in mixed continuous and discrete data. This model, referred to as C-ADDICT, builds upon the experiences of our previous ADDICT algorithm. It can handle discrete and continuous data jointly, is intrinsically shift-invariant, and crucially, it encodes each input signal (either continuous or discrete) from a joint activation and uniform combinations of filters, allowing the correlation across the input signals to be captured. The performance of C-ADDICT, is evaluated on a representative dataset composed of real spacecraft telemetries with an available ground-truth, providing promising results.

Aircraft certification procedures require the estimation of wing deformation, which is a very challenging problem in photogrammetry applications. Indeed, in real flight conditions with varying environment, 3D reconstruction is strongly degraded. To cope with this issue, we propose to introduce prior knowledge about the wing mechanical limits in the photogrammetry reconstruction method. These mechanical limits are expressed as appropriate regularizations that are included into the classical bundle adjustment step. The proposed approach is evaluated using data acquired on a real aircraft yielding promising results.

This paper introduces a novel algorithm for the fusion of magnetic resonance and ultrasound images, based on a patch-wise polynomial model relating the gray levels of the two imaging systems (called modalities). Starting from observation models adapted to each modality and exploiting a patch-wise polynomial model, the fusion problem is expressed as the minimization of a cost function including two data fidelity terms and two regularizations. This minimization is performed using a PALM-based algorithm, given its ability to handle nonlinear and possibly non-convex functions. The efficiency of the proposed method is evaluated on phantom data. The resulting fused image is shown to contain complementary information from both magnetic resonance (MR) and ultrasound (US) images, i.e., with a good contrast (as for the MR image) and a good spatial resolution (as for the US image).

This paper introduces a new fusion method for magnetic resonance (MR) and ultrasound (US) images, which aims at combining the advantages of each modality, i.e., good contrast and signal to noise ratio for the MR image and good spatial resolution for the US image. The proposed algorithm is based on two inverse problems, performing a super-resolution of the MR image and a denoising of the US image. A polynomial function is introduced to model the relationships between the gray levels of the two modalities. The resulting inverse problem is solved using a proximal alternating linearized minimization framework. The accuracy and the interest of the fusion algorithm are shown quantitatively and qualitatively via evaluations on synthetic and experimental phantom data.

Single-photon light detection and ranging (Lidar) data can be used to capture depth and intensity profiles of a 3D scene. In a general setting, the scenes can have an unknown number of surfaces per pixel (semi-transparent surfaces or outdoor measurements), high background noise (strong ambient illumination), can be acquired by systems with a broad instrumental response (non-parallel laser beam with respect to the target surface) and with possibly high attenuating media (underwater conditions). The existing methods generally tackle only a subset of these problems and can fail in a more general scenario. In this paper, we propose a new 3D reconstruction algorithm that can handle all the aforementioned difficulties. The novel algorithm estimates the broadening of the impulse response, considers the attenuation induced by scattering media, while allowing for multiple surfaces per pixel. A series of experiments performed in real long-range and underwater Lidar datasets demonstrate the performance of the proposed method.

The identification of nonlinear Wiener models (NWMs) for deterministic inputs and Gaussian noise is studied. We show that the nonparametric kernel regression estimation of the nonlinearity of a NWM (based on the Nadaraya-Watson kernel estimator) can be formulated as a parametric estimation problem leading to a Gaussian conditional observation model. This property allows us to derive the maximum likelihood estimators of the unknown parameters of the NWM, as well as the associated Cramér-Rao (CR) bounds. We finally derive a CR-like bound on the global mean squared error (MSE) of the estimated nonlinearity of a NWM. Numerical results obtained for a pulse wave input are presented and compared to the ones based on the Nadaraya-Watson kernel estimator.

Light detection and ranging (Lidar) data can be used to capture the depth and intensity profile of a 3D scene. This modality relies on constructing, for each pixel, a histogram of time delays between emitted light pulses and detected photon arrivals. In a general setting, more than one surface can be observed in a single pixel. The problem of estimating the number of surfaces, their reflectivity, and position becomes very challenging in the low-photon regime (which equates to short acquisition times) or relatively high background levels (i.e., strong ambient illumination). This paper presents a new approach to 3D reconstruction using single-photon, single-wavelength Lidar data, which is capable of identifying multiple surfaces in each pixel. Adopting a Bayesian approach, the 3D structure to be recovered is modelled as a marked point process, and reversible jump Markov chain Monte Carlo (RJ-MCMC) moves are proposed to sample the posterior distribution of interest. In order to promote spatial correlation between points belonging to the same surface, we propose a prior that combines an area interaction process and a Strauss process. New RJ-MCMC dilation and erosion updates are presented to achieve an efficient exploration of the configuration space. To further reduce the computational load, we adopt a multiresolution approach, processing the data from a coarse to the finest scale. The experiments performed with synthetic and real data show that the algorithm obtains better reconstructions than other recently published optimization algorithms for lower execution times.

Joint deconvolution and segmentation of ultrasound images is a challenging problem in medical imaging. By adopting a hierarchical Bayesian model, we propose an accelerated Markov chain Monte Carlo scheme where the tissue reflectivity function is sampled thanks to a recently introduced proximal unadjusted Langevin algorithm. This new approach is combined with a forward-backward step and a preconditioning strategy to accelerate the convergence, and with a method based on the majorization-minimization principle to solve the inner nonconvex minimization problems. As demonstrated in numerical experiments conducted on both simulated and in vivo ultrasound images, the proposed method provides high-quality restoration and segmentation results and is up to six times faster than an existing Hamiltonian Monte Carlo method.

So far, the problem of unmixing large or multitemporal hyperspectral data sets has been specifically addressed in the remote sensing literature only by a few dedicated strategies. Among them, some attempts have been made within a distributed estimation framework, in particular, relying on the alternating direction method of multipliers. In this paper, we propose to study the interest of a partially asynchronous distributed unmixing procedure based on a recently proposed asynchronous algorithm. Under standard assumptions, the proposed algorithm inherits its convergence properties from recent contributions in nonconvex optimization, while allowing the problem of interest to be efficiently addressed. Comparisons with a distributed synchronous counterpart of the proposed unmixing procedure allow its interest to be assessed on synthetic and real data. Besides, thanks to its genericity and flexibility, the procedure investigated in this paper can be implemented to address various matrix factorization problems.

In the past years, one common way of enhancing the spatial resolution of a hyperspectral (HS) image has been to fuse it with complementary information coming from multispectral (MS) or panchromatic images. This paper proposes a new method for reconstructing a high-spatial, high-spectral image from measurements acquired after compressed sensing by multiple sensors of different spectral ranges and spatial resolutions, with specific attention to HS and MS compressed images. To solve this problem, we introduce a fusion model based on the linear spectral unmixing model classically used for HS images and investigate an optimization algorithm based on a block coordinate descent strategy. The nonnegative and sum-to-one constraints resulting from the intrinsic physical properties of abundances as well as a total variation penalization are used to regularize this ill-posed inverse problem. Simulation results conducted on realistic compressed HS and MS images show that the proposed algorithm can provide fusion results that are very close to those obtained with uncompressed images, with the advantage of using a significantly reduced number of measurements.

Compressive spectral imagers reduce the number of sampled pixels by coding and combining the spectral information. However, sampling compressed information with simultaneous high spatial and high spectral resolution demands expensive high-resolution sensors. This work introduces a model allowing data from high spatial/low spectral and low spatial/high spectral resolution compressive sensors to be fused. Based on this model, the compressive fusion process is formulated as an inverse problem that minimizes an objective function defined as the sum of a quadratic data fidelity term and smoothness and sparsity regularization penalties. The parameters of the different sensors are optimized and the choice of an appropriate regularization is studied in order to improve the quality of the high resolution reconstructed images. Simulation results conducted on synthetic and real data, with different CS imagers, allow the quality of the proposed fusion method to be appreciated.

Multipath (MP) remains the main source of error when using global navigation satellite systems (GNSS) in a constrained environment, leading to biased measurements and thus to inaccurate estimated positions. This paper formulates the GNSS navigation problem as the resolution of an overdetermined system whose unknowns are the receiver position and speed, clock bias and clock drift, and the potential biases affecting GNSS measurements. We assume that only a part of the satellites are affected by MP, i.e., that the unknown bias vector has several zero components, which allows sparse estimation theory to be exploited. The natural way of enforcing this sparsity is to introduce an ℓ1regularization associated with the bias vector. This leads to a least absolute shrinkage and selection operator problem that is solved using a reweighted-ℓ1algorithm. The weighting matrix of this algorithm is designed carefully as functions of the satellite carrier-to-noise density ratio (C/N0) and the satellite elevations. Experimental validation conducted with real GPS data show the effectiveness of the proposed method as long as the sparsity assumption is respected.

Available super-resolution techniques for 3-D images are either computationally inefficient prior-knowledge-based iterative techniques or deep learning methods which require a large database of known low-resolution and high-resolution image pairs. A recently introduced tensor-factorization-based approach offers a fast solution without the use of known image pairs or strict prior assumptions. In this paper, this factorization framework is investigated for single image resolution enhancement with an offline estimate of the system point spread function. The technique is applied to 3-D cone beam computed tomography for dental image resolution enhancement. To demonstrate the efficiency of our method, it is compared to a recent state-of-the-art iterative technique using low-rank and total variation regularizations. In contrast to this comparative technique, the proposed reconstruction technique gives a 2-order-of-magnitude improvement in running time-2 min compared to 2 h for a dental volume of 282×266×392 voxels. Furthermore, it also offers slightly improved quantitative results (peak signal-to-noise ratio and segmentation quality). Another advantage of the presented technique is the low number of hyperparameters. As demonstrated in this paper, the framework is not sensitive to small changes in its parameters, proposing an ease of use.

This paper introduces a robust 2-D cardiac motion estimation method. The problem is formulated as an energy minimization with an optical flow-based data fidelity term and two regularization terms imposing spatial smoothness and the sparsity of the motion field in an appropriate cardiac motion dictionary. Robustness to outliers, such as imaging artefacts and anatomical motion boundaries, is introduced using robust weighting functions for the data fidelity term as well as for the spatial and sparse regularizations. The motion fields and the weights are computed jointly using an iteratively re-weighted minimization strategy. The proposed robust approach is evaluated on synthetic data and realistic simulation sequences with available ground-truth by comparing the performance with state-of-the-art algorithms. Finally, the proposed method is validated using two sequences of in vivo images. The obtained results show the interest of the proposed approach for 2-D cardiac ultrasound imaging.

Multipath remains the main source of error when using global navigation satellite systems (GNSS) in constrained environment, leading to biased measurements and thus to inaccurate estimated positions. This paper formulates the GNSS navigation problem as the resolution of an overdetermined system, which depends nonlinearly on the receiver position and linearly on the clock bias and drift, and possible biases affecting GNSS measurements. The extended Kalman filter is used to linearize the navigation problem whereas sparse estimation is considered to estimate multipath biases. We assume that only a part of the satellites are affected by multipath, i.e., that the unknown bias vector is sparse in the sense that several of its components are equal to zero. The natural way of enforcing sparsity is to introduce an I1regularization associated with the bias vector. This leads to a least absolute shrinkage and selection operator (LASSO) problem that is solved using a reweighted I1algorithm. The weighting matrix of this algorithm is designed carefully as functions of the satellite carrier to noise density ratio and the satellite elevations. The smooth variations of multipath biases versus time are enforced using a regularization based on total variation. An experiment conducted on real data allows the performance of the proposed method to be appreciated.

This paper studies the performance of the generalized likelihood ratio test (GLRT) for the conditional signal model. By conditional signal model, we mean that under both hypotheses, the observations are a linear superposition of unknown deterministic signals corrupted by additive noise, with a mixing matrix depending on an unknown deterministic parameter vector. The contribution of this work is the derivation of closed form expressions for the probabilities of false alarm and of detection of the GLRT at high signal-to-noise ratio, allowing the receiver operating characteristic of the GLRT to be computed analytically. The most general case is tackled, i.e., when the number of unknown signals and the number of unknown deterministic parameters of the mixing matrix are allowed to be different under the two hypotheses.

Texture characterization of natural images using the mathematical framework of multifractal analysis (MFA) enables the study of the fluctuations in the regularity of image intensity. Although successfully applied in various contexts, the use of MFA has so far been limited to the independent analysis of a single image, while the data available in applications are increasingly multivariate. This paper addresses this limitation and proposes a joint Bayesian model and associated estimation procedure for multifractal parameters of multivariate images. It builds on a recently introduced generic statistical model that enabled the Bayesian estimation of multifractal parameters for a single image and relies on the following original key contributions: First, we develop a novel Fourier domain statistical model for a single image that permits the use of a likelihood that is separable in the multifractal parameters via data augmentation. Second, a joint Bayesian model for multivariate images is formulated in which prior models based on gamma Markov random fields encode the assumption of the smooth evolution of multifractal parameters between the image components. The design of the likelihood and of conjugate prior models is such that exploitation of the conjugacy between the likelihood and prior models enables an efficient estimation procedure that can handle a large number of data components. Numerical simulations conducted using sequences of multifractal images demonstrate that the proposed procedure significantly outperforms previous univariate benchmark formulations at a competitive computational cost.

This paper introduces a new method for cardiac motion estimation in 2-D ultrasound images. The motion estimation problem is formulated as an energy minimization, whose data fidelity term is built using the assumption that the images are corrupted by multiplicative Rayleigh noise. In addition to a classical spatial smoothness constraint, the proposed method exploits the sparse properties of the cardiac motion to regularize the solution via an appropriate dictionary learning step. The proposed method is evaluated on one data set with available ground-truth, including four sequences of highly realistic simulations. The approach is also validated on both healthy and pathological sequences of in vivo data. We evaluate the method in terms of motion estimation accuracy and strain errors and compare the performance with state-of-the-art algorithms. The results show that the proposed method gives competitive results for the considered data. Furthermore, the in vivo strain analysis demonstrates that meaningful clinical interpretation can be obtained from the estimated motion vectors.

This paper derives lower bounds for the mean square errors of parameter estimators in the case of Poisson distributed data subjected to multiple abrupt changes. Since both change locations (discrete parameters) and parameters of the Poisson distribution (continuous parameters) are unknown, it is appropriate to consider a mixed Cramér-Rao/Weiss-Weinstein bound for which we derive closed-form expressions and illustrate its tightness by numerical simulations.

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This paper introduces a hierarchical Bayesian model for the reconstruction of hyperspectral images using compressed sensing measurements. This model exploits known properties of natural images, promoting the recovered image to be sparse on a selected basis and smooth in the image domain. The posterior distribution of this model is too complex to derive closed form expressions for the estimators of its parameters. Therefore, an MCMC method is investigated to sample this posterior distribution. The resulting samples are used to estimate the unknown model parameters and hyperparameters in an unsupervised framework. The results obtained on real data illustrate the improvement in reconstruction quality when compared to some existing techniques.

Compressive spectral imagers drastically reduce the number of sampled pixels by performing linear combinations of coded spectral information. However, compressing information with simultaneously high spatial and high spectral resolutions demands expensive high-resolution sensors. This work introduces a model allowing compressive data from high spatial/low spectral and low spatial/high spectral resolution sensors to be fused. The sensing matrix of this model is designed carefully to be incoherent with the dictionary associated with the unknown image. Based on this model, the compressive fusion process is formulated as an inverse problem that minimizes an objective function defined as the sum of a quadratic data fidelity term and smoothness and sparsity regularization penalties.

This paper investigates a new method for cardiac motion estimation in 2D ultrasound images. The motion estimation problem is formulated as an energy minimization with spatial and sparse regularizations. In addition to a classical spatial smoothness constraint, the proposed method exploits the sparse properties of the cardiac motion to regularize the solution via an appropriate dictionary learning step. The proposed method is evaluated in terms of motion estimation and strain accuracy and compared with state-of-the-art algorithms using a dataset of realistic simulations. These simulation results show that the proposed method provides very promising results for myocardial motion estimation.

This paper studies a new three-step procedure for detecting anomalies in crop development using temporal indicators derived from multispectral satellite images. These anomalies may result from seeding problems, heterogeneity, deficiency and stress. The first step estimates different biophysical and statistical parameters associated with these parameters from the observed images. In a second step, missing data that arise from the existence of clouds or limited coverage in the satellite image are reconstructed. Finally, the mean shift algorithm is used as an unsupervised classifier to detect anomalies in these reconstructed data. The proposed procedure is evaluated using agronomic indicators estimated from SPOT 5 Take 5 satellite images from the Beauce area in France.

In the community of remote sensing, nonlinear mixture models have recently received particular attention in hyperspectral image processing. In this paper, we present a novel nonlinear spectral unmixing method following the recent multilinear mixing model of Heylen and Scheunders, which includes an infinite number of terms related to interactions between different endmembers. The proposed unmixing method is unsupervised in the sense that the endmembers are estimated jointly with the abundances and other parameters of interest, i.e., the transition probability of undergoing further interactions. Nonnegativity and sum-to-one constraints are imposed on abundances while only nonnegativity is considered for endmembers. The resulting unmixing problem is formulated as a constrained nonlinear optimization problem, which is solved by a block coordinate descent strategy, consisting of updating the end-members, abundances, and transition probability iteratively. The proposed method is evaluated and compared with existing linear and nonlinear unmixing methods for both synthetic and real hyperspectral data sets acquired by the airborne visible/infrared imaging spectrometer sensor. The advantage of using nonlinear unmixing as opposed to linear unmixing is clearly shown in these examples.

Recent work has shown that existing powerful Bayesian hyperspectral unmixing algorithms can be significantly improved by incorporating the inherent local spatial correlations between pixel class labels via the use of Markov random fields. We here propose a new Bayesian approach to joint hyperspectral unmixing and image classification such that the previous assumption of stochastic abundance vectors is relaxed to a formulation whereby a common abundance vector is assumed for pixels in each class. This allows us to avoid stochastic reparameterizations and, instead, we propose a symmetric Dirichlet distributionmodel with adjustable parameters for the common abundance vector of each class. Inference over the proposed model is achieved via a hybrid Gibbs sampler, and in particular, simulated annealing is introduced for the label estimation in order to avoid the local-trap problem. Experiments on a synthetic image and a popular, publicly available real data set indicate the proposed model is faster than and outperforms the existing approach quantitatively and qualitatively. Moreover, for appropriate choices of the Dirichlet parameter, it is shown that the proposed approach has the capability to induce sparsity in the inferred abundance vectors. It is demonstrated that this offers increased robustness in cases where the preprocessing endmember extraction algorithms overestimate the number of active endmembers present in a given scene.

In complex environments, the presence or absence of multipath signals not only depends on the relative motion between the GNSS receiver and navigation satellites, but also on the environment where the receiver is located. Thus it is difficult to use a specific propagation model to accurately capture the dynamics of multipath signal parameters when the GNSS receiver is moving in urban canyons or other severe obstructions. This paper introduces a statistical model for the line-of-sight and multipath signals received by a GNSS receiver. A multi-correlator based GNSS receiver is also exploited with the advantage to fully characterizing the impact of multipath signals on the correlation function by providing samples of the whole correlation function. Finally, a maximum likelihood-based unscented Kalman filter is investigated to estimate the line-of-sight and multipath signal parameters. Numerical simulations clearly validate the effectiveness of the proposed approach.

Texture analysis is an image processing task that can be conducted using the mathematical framework of multifractal analysis to study the regularity fluctuations of image intensity and the practical tools for their assessment, such as (wavelet) leaders. A recently introduced statistical model for leaders enables the Bayesian estimation of multifractal parameters. It significantly improves performance over standard (linear regression based) estimation. However, the computational cost induced by the associated nonstandard posterior distributions limits its application. The present work proposes an alternative Bayesian model for multifractal analysis that leads to more efficient algorithms. It relies on three original contributions: A novel generative model for the Fourier coefficients of log-leaders; an appropriate reparametrization for handling its inherent constraints; a data-augmented Bayesian model yielding standard conditional posterior distributions that can be sampled exactly. Numerical simulations using synthetic multifractal images demonstrate the excellent performance of the proposed algorithm, both in terms of estimation quality and computational cost.

Hyperspectral unmixing consists in determining the reference spectral signatures composing a hyperspectral image and their relative abundance fractions in each pixel. In practice, the identified signatures may be affected by a significant spectral variability resulting for instance from the temporal evolution of the imaged scene. This phenomenon can be accounted for by using a perturbed linear mixing model. This paper studies an online estimation algorithm for the parameters of this extended linear mixing model. This algorithm is of interest for the practical applications where the size of the hyper-spectral images precludes the use of batch procedures. The performance of the proposed method is evaluated on synthetic data.

Texture analysis can be embedded in the mathematical framework of multifractal (MF) analysis, enabling the study of the fluctuations in regularity of image intensity and providing practical tools for their assessment, wavelet leaders. A statistical model for leaders was proposed permitting Bayesian estimation of MF parameters for images yielding improved estimation quality over linear regression based estimation. This present work proposes an extension of this Bayesian model for patch-wise MF analysis of images. Classical MF analysis assumes space homogeneity of the MF properties whereas here we assume MF properties may change between texture elements and we do not know where the changes are located. This paper proposes a joint Bayesian model for patches formulated using spatially smoothing gamma Markov Random Field priors to counterbalance the increased statistical variability of estimates caused by small patch sizes. Numerical simulations based on synthetic multi-fractal images demonstrate that the proposed algorithm outperforms previous formulations and standard estimators.

The SPOT 6-7 satellite ground segment includes a systematic and automatic cloud detection step in order to feed a catalogue with a binary cloud mask and an appropriate confidence measure. In order to significantly improve the SPOT cloud detection and get rid of frequent manual re-labelings, we study a new automatic cloud detection technique that is adapted to large datasets. The proposed method is based on a modified distributed boosting algorithm. Experiments conducted using the framework Apache Spark on a SPOT 6 image database with various landscapes and cloud coverage show promising results.

In recent years, remote sensing of the Earth surface using images acquired from aircraft or satellites has gained a lot of attention. The acquisition technology has been evolving fast and, as a consequence, many different kinds of sensors (e.g., optical, radar, multispectral, and hyperspectral) are now available to capture different features of the observed scene. One of the main objectives of remote sensing is to monitor changes on the Earth surface. Change detection has been thoroughly studied in the case of images acquired by the same sensors (mainly optical or radar sensors). However, due to the diversity and complementarity of the images, change detection between images acquired with different kinds of sensors (sometimes referred to as heterogeneous sensors) is clearly an interesting problem. A statistical model and a change detection strategy were recently introduced in [J. Prendes, M. Chabert, F. Pascal, A. Giros, and J.-Y. Tourneret, Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Florence, Italy, 2014; IEEE Trans. Image Process., 24 (2015), pp. 799--812] to deal with images captured by heterogeneous sensors. The main idea of the suggested strategy was to model the objects contained in an analysis window by mixtures of distributions. The manifold defined by these mixtures was then learned using training data belonging to unchanged areas. The changes were finally detected by thresholding an appropriate distance to the estimated manifold. This paper goes a step further by introducing a Bayesian nonparametric framework allowing us to deal with an unknown number of objects in analysis windows without specifying an upper bound for this number. A Markov random field is also introduced to account for the spatial correlation between neighboring pixels. The proposed change detector is validated using different sets of synthetic and real images (including pairs of optical images and pairs of optical and radar images) showing a significant improvement when compared to existing algorithms.

This letter proposes a robust fast multiband image fusion method to merge a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. Following the method recently developed by Wei et al., the generalized Sylvester matrix equation associated with the multiband image fusion problem is solved in a more robust and efficient way by exploiting the Woodbury formula, avoiding any permutation operation in the frequency domain as well as the blurring kernel invertibility assumption required in their method. Thanks to this improvement, the proposed algorithm requires fewer computational operations and is also more robust with respect to the blurring kernel compared with the one developed by Wei et al. The proposed new algorithm is tested with different priors considered by Wei et al. Our conclusion is that the proposed fusion algorithm is more robust than the one by Wei et al. with a reduced computational cost.

Linear mixture models are commonly used to represent a hyperspectral data cube as linear combinations of endmember spectra. However, determining the number of endmembers for images embedded in noise is a crucial task. This paper proposes a fully automatic approach for estimating the number of endmembers in hyperspectral images. The estimation is based on recent results of random matrix theory related to the so-called spiked population model. More precisely, we study the gap between successive eigenvalues of the sample covariance matrix constructed from high-dimensional noisy samples. The resulting estimation strategy is fully automatic and robust to correlated noise owing to the consideration of a noise-whitening step. This strategy is validated on both synthetic and real images. The experimental results are very promising and show the accuracy of this algorithm with respect to state-of-the-art algorithms.

This paper proposes a new Bayesian strategy for the smooth estimation of altimetric parameters. The altimetric signal is assumed to be corrupted by a thermal and speckle noise distributed according to an independent and non-identically Gaussian distribution. We introduce a prior enforcing a smooth temporal evolution of the altimetric parameters which improves their physical interpretation. The posterior distribution of the resulting model is optimized using a gradient descent algorithm which allows us to compute the maximum a posteriori estimator of the unknown model parameters. This algorithm has a low computational cost that is suitable for real-time applications. The proposed Bayesian strategy and the corresponding estimation algorithm are evaluated using both synthetic and real data associated with conventional and delay/Doppler altimetry. The analysis of real Jason-2 and CryoSat-2 waveforms shows an improvement in parameter estimation when compared to state-of-the-art estimation algorithms.

This paper presents a multiband image fusion algorithm based on unsupervised spectral unmixing for combining a high-spatial-low-spectral-resolution image and a low-spatial-high-spectral-resolution image. The widely used linear observation model (with additive Gaussian noise) is combined with the linear spectral mixture model to form the likelihoods of the observations. The nonnegativity and sum-to-one constraints resulting from the intrinsic physical properties of the abundances are introduced as prior information to regularize this ill-posed problem. The joint fusion and unmixing problem is then formulated as maximizing the joint posterior distribution with respect to the endmember signatures and abundance maps. This optimization problem is attacked with an alternating optimization strategy. The two resulting subproblems are convex and are solved efficiently using the alternating direction method of multipliers. Experiments are conducted for both synthetic and semi-real data. Simulation results show that the proposed unmixing-based fusion scheme improves both the abundance and endmember estimation compared with the state-of-the-art joint fusion and unmixing algorithms.

This paper presents a new strategy to correct the Earth data corrupted by spurious samples that are randomly included in the multiplexed data stream provided by the MADRAS instrument. The proposed strategy relies on the construction of a trellis associated with each scan of the multichannel image, modeling the possible occurrences of these erroneous data. A specific weight that promotes the smooth behavior of the signals recorded in each channel is assigned to each transition between trellis states. The joint detection and correction of the erroneous data are conducted using a dynamic programming algorithm for minimizing the overall cost function throughout the trellis. Simulation results obtained on synthetic and real MADRAS data demonstrate the effectiveness of the proposed solution.

Mixing phenomena in hyperspectral images depend on a variety of factors, such as the resolution of observation devices, the properties of materials, and how these materials interact with incident light in the scene. Different parametric and nonparametric models have been considered to address hyperspectral unmixing problems. The simplest one is the linear mixing model. Nevertheless, it has been recognized that the mixing phenomena can also be nonlinear. The corresponding nonlinear analysis techniques are necessarily more challenging and complex than those employed for linear unmixing. Within this context, it makes sense to detect the nonlinearly mixed pixels in an image prior to its analysis, and then employ the simplest possible unmixing technique to analyze each pixel. In this paper, we propose a technique for detecting nonlinearly mixed pixels. The detection approach is based on the comparison of the reconstruction errors using both a Gaussian process regression model and a linear regression model. The two errors are combined into a detection statistics for which a probability density function can be reasonably approximated. We also propose an iterative endmember extraction algorithm to be employed in combination with the detection algorithm. The proposed detect-then-unmix strategy, which consists of extracting endmembers, detecting nonlinearly mixed pixels and unmixing, is tested with synthetic and real images.

Hyperspectral unmixing is aimed at identifying the reference spectral signatures composing a hyperspectral image and their relative abundance fractions in each pixel. In practice, the identified signatures may vary spectrally from an image to another due to varying acquisition conditions, thus inducing possibly significant estimation errors. Against this background, the hyperspectral unmixing of several images acquired over the same area is of considerable interest. Indeed, such an analysis enables the endmembers of the scene to be tracked and the corresponding endmember variability to be characterized. Sequential endmember estimation from a set of hyperspectral images is expected to provide improved performance when compared with methods analyzing the images independently. However, the significant size of the hyperspectral data precludes the use of batch procedures to jointly estimate the mixture parameters of a sequence of hyperspectral images. Provided that each elementary component is present in at least one image of the sequence, we propose to perform an online hyperspectral unmixing accounting for temporal endmember variability. The online hyperspectral unmixing is formulated as a two-stage stochastic program, which can be solved using a stochastic approximation. The performance of the proposed method is evaluated on synthetic and real data. Finally, a comparison with independent unmixing algorithms illustrates the interest of the proposed strategy.

This paper proposes a joint segmentation and deconvolution Bayesian method for medical ultrasound (US) images. Contrary to piecewise homogeneous images, US images exhibit heavy characteristic speckle patterns correlated with the tissue structures. The generalized Gaussian distribution (GGD) has been shown to be one of the most relevant distributions for characterizing the speckle in US images. Thus, we propose a GGD-Potts model defined by a label map coupling US image segmentation and deconvolution. The Bayesian estimators of the unknown model parameters, including the US image, the label map, and all the hyperparameters are difficult to be expressed in a closed form. Thus, we investigate a Gibbs sampler to generate samples distributed according to the posterior of interest. These generated samples are finally used to compute the Bayesian estimators of the unknown parameters. The performance of the proposed Bayesian model is compared with the existing approaches via several experiments conducted on realistic synthetic data and in vivo US images.

This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high-resolution image from its blurred, decimated, and noisy version. The existing algorithms for single image SR use different strategies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution is derived and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an l2 -regularized quadratic model, i.e., an l2 - l2 optimization problem. The flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded into traditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with existing techniques.

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This paper presents an unsupervised Bayesian algorithm for hyperspectral image unmixing accounting for endmember variability. Each image pixel is modeled by a linear combination of random endmembers to take into account endmember variability in the image. The coefficients of this linear combination (referred to as abundances) allow the proportions of each material (endmembers) to be quantified in the image pixel. An additive noise is also considered in the proposed model generalizing the normal compositional model. The proposed Bayesian algorithm exploits spatial correlations between adjacent pixels of the image and provides spectral information by achieving a spectral unmixing. It estimates both the mean and the covariance matrix of each endmember in the image. A spatial classification is also obtained based on the estimated abundances. Simulations conducted with synthetic and real data show the potential of the proposed model and the unmixing performance for the analysis of hyperspectral images.

This paper proposes a new Bayesian strategy for the estimation of smooth parameters from nonlinear models. The observed signal is assumed to be corrupted by an independent and non identically (colored) Gaussian distribution. A prior enforcing a smooth temporal evolution of the model parameters is considered. The joint posterior distribution of the unknown parameter vector is then derived. A Gibbs sampler coupled with a Hamiltonian Monte Carlo algorithm is proposed which allows samples distributed according to the posterior of interest to be generated and to estimate the unknown model parameters/hyperparameters. Simulations conducted with synthetic and real satellite altimetric data show the potential of the proposed Bayesian model and the corresponding estimation algorithm for nonlinear regression with smooth estimated parameters.

This paper introduces a Bayesian non parametric (BNP) model associated with a Markov random field (MRF) for detecting changes between remote sensing images acquired by homogeneous or heterogeneous sensors. The proposed model is built for an analysis window which takes advantage of the spatial information via an MRF. The model does not require any a priori knowledge about the number of objects contained in the window thanks to the BNP framework. The change detection strategy can be divided into two steps. First, the segmentation of the two images is performed using a region based approach. Second, the joint statistical properties of the objects in the two images allows an appropriate manifold to be defined. This manifold describes the relationships between the different sensor responses to the observed scene and can be learnt from a training unchanged area. It allows us to build a similarity measure between the images that can be used in many applications such as change detection or image registration. Simulation results conducted on synthetic and real optical and synthetic aperture radar (SAR) images show the efficiency of the proposed method for change detection.

Delay/Doppler altimetry (DDA) aims at reducing the measurement noise and increasing the along-track resolution in comparison with conventional pulse-limited altimetry. In a previous paper, we have proposed a semi-analytical model for DDA, which considers some simplifications as the absence of mispointing antenna. This paper first proposes a new analytical expression for the flat surface impulse response (FSIR), considering antenna mispointing angles, a circular antenna pattern, no vertical speed effect, and uniform scattering. The 2-D delay/Doppler map is then obtained by a numerical computation of the convolution between the proposed analytical function, the probability density function of the heights of the specular scatterers, and the time/frequency point target response of the radar. The approximations used to obtain the semi-analytical model are analyzed, and the associated errors are quantified by analytical bounds for these errors. The second contribution of this paper concerns the estimation of the parameters associated with the multilook semi-analytical model. Two estimation strategies based on the least squares procedure are proposed. The proposed model and algorithms are validated on both synthetic and real waveforms. The obtained results are very promising and show the accuracy of this generalized model with respect to the previous model assuming zero antenna mispointing.

This paper presents a variational-based approach for fusing hyperspectral and multispectral images. The fusion problem is formulated as an inverse problem whose solution is the target image assumed to live in a lower dimensional subspace. A sparse regularization term is carefully designed, relying on a decomposition of the scene on a set of dictionaries. The dictionary atoms and the supports of the corresponding active coding coefficients are learned from the observed images. Then, conditionally on these dictionaries and supports, the fusion problem is solved via alternating optimization with respect to the target image (using the alternating direction method of multipliers) and the coding coefficients. Simulation results demonstrate the efficiency of the proposed algorithm when compared with state-of-the-art fusion methods.

Texture characterization is a central element in many image processing applications. Multifractal analysis is a useful signal and image processing tool, yet, the accurate estimation of multifractal parameters for image texture remains a challenge. This is due in the main to the fact that current estimation procedures consist of performing linear regressions across frequency scales of the 2D dyadic wavelet transform, for which only a few such scales are computable for images. The strongly non-Gaussian nature of multifractal processes, combined with their complicated dependence structure, makes it difficult to develop suitable models for parameter estimation. Here, we propose a Bayesian procedure that addresses the difficulties in the estimation of the multifractality parameter. The originality of the procedure is threefold. The construction of a generic semiparametric statistical model for the logarithm of wavelet leaders; the formulation of Bayesian estimators that are associated with this model and the set of parameter values admitted by multifractal theory; the exploitation of a suitable Whittle approximation within the Bayesian model which enables the otherwise infeasible evaluation of the posterior distribution associated with the model. Performance is assessed numerically for several 2D multifractal processes, for several image sizes and a large range of process parameters. The procedure yields significant benefits over current benchmark estimators in terms of estimation performance and ability to discriminate between the two most commonly used classes of multifractal process models. The gains in performance are particularly pronounced for small image sizes, notably enabling for the first time the analysis of image patches as small as 64 × 64 pixels.

This paper presents an unsupervised Bayesian algorithm for hyperspectral image unmixing, accounting for endmember variability. The pixels are modeled by a linear combination of endmembers weighted by their corresponding abundances. However, the endmembers are assumed random to consider their variability in the image. An additive noise is also considered in the proposed model, generalizing the normal compositional model. The proposed algorithm exploits the whole image to benefit from both spectral and spatial information. It estimates both the mean and the covariance matrix of each endmember in the image. This allows the behavior of each material to be analyzed and its variability to be quantified in the scene. A spatial segmentation is also obtained based on the estimated abundances. In order to estimate the parameters associated with the proposed Bayesian model, we propose to use a Hamiltonian Monte Carlo algorithm. The performance of the resulting unmixing strategy is evaluated through simulations conducted on both synthetic and real data.

Remote sensing images are commonly used to monitor the earth surface evolution. This surveillance can be conducted by detecting changes between images acquired at different times and possibly by different kinds of sensors. A representative case is when an optical image of a given area is available and a new image is acquired in an emergency situation (resulting from a natural disaster for instance) by a radar satellite. In such a case, images with heterogeneous properties have to be compared for change detection. This paper proposes a new approach for similarity measurement between images acquired by heterogeneous sensors. The approach exploits the considered sensor physical properties and specially the associated measurement noise models and local joint distributions. These properties are inferred through manifold learning. The resulting similarity measure has been successfully applied to detect changes between many kinds of images, including pairs of optical images and pairs of optical-radar images.

This paper proposes a fast multi-band image fusion algorithm, which combines a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The well admitted forward model is explored to form the likelihoods of the observations. Maximizing the likelihoods leads to solving a Sylvester equation. By exploiting the properties of the circulant and downsampling matrices associated with the fusion problem, a closed-form solution for the corresponding Sylvester equation is obtained explicitly, getting rid of any iterative update step. Coupled with the alternating direction method of multipliers and the block coordinate descent method, the proposed algorithm can be easily generalized to incorporate prior information for the fusion problem, allowing a Bayesian estimator. Simulation results show that the proposed algorithm achieves the same performance as the existing algorithms with the advantage of significantly decreasing the computational complexity of these algorithms.

This paper presents a nonlinear mixing model for joint hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are linear mixtures of endmembers, corrupted by an additional nonlinear term and an additive Gaussian noise. A Markov random field is considered for nonlinearity detection based on the spatial structure of the nonlinear terms. The observed image is segmented into regions where nonlinear terms, if present, share similar statistical properties. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint nonlinear unmixing and nonlinearity detection algorithm. Simulations conducted with synthetic and real data show the accuracy of the proposed unmixing and nonlinearity detection strategy for the analysis of hyperspectral images.

Sparse signal/image recovery is a challenging topic that has captured a great interest during the last decades. To address the ill-posedness of the related inverse problem, regularization is often essential by using appropriate priors that promote the sparsity of the target signal/image. In this context, ℓ0+ ℓ1regularization has been widely investigated. In this paper, we introduce a new prior accounting simultaneously for both sparsity and smoothness of restored signals. We use a Bernoulli-generalized Gauss-Laplace distribution to perform ℓ0+ ℓ1+ ℓ2regularization in a Bayesian framework. Our results show the potential of the proposed approach especially in restoring the non-zero coefficients of the signal/image of interest.

This paper investigates the use of Gaussian processes to detect non-linearly mixed pixels in hyperspectral images. The proposed technique is independent of nonlinear mixing mechanism, and therefore is not restricted to any prescribed nonlinear mixing model. The observed reflectances are estimated using both the least squares method and a Gaussian process. The fitting errors of the two approaches are combined in a test statistics for which it is possible to estimate a detection threshold given a required probability of false alarm. The proposed detector is compared to a robust nonlinearity detector recently proposed using synthetic data and is shown to provide a better detection performance. The new detector is also tested on a real hyperspectral image.

This paper introduces a new statistical model for homogeneous images acquired by the same kind of sensor (e.g., two optical images) and heterogeneous images acquired by different sensors (e.g., optical and synthetic aperture radar (SAR) images). The proposed model assumes that each image pixel is distributed according to a mixture of multi-dimensional distributions depending on the noise properties and on the transformation between the actual scene and the image intensities. The parameters of this new model can be estimated by the classical expectation-maximization algorithm. The estimated parameters are finally used to learn the relationships between the different images. This information can be used in many image processing applications, particularly those requiring a similarity measure (e.g., change detection or registration). Simulation results on synthetic and real images show the potential of the proposed model. A brief application to change detection between optical and SAR images is finally investigated.

This paper deals with the demodulation of automatic identification system (AIS) signals received by a satellite. More precisely, an error correction algorithm is presented, whose computational complexity is reduced with respect to that of a previously considered approach. This latter approach makes use of the cyclic redundancy check (CRC) of a message as redundancy, in order to correct transmission errors. In this paper, the CRC is also considered as a correction tool, but only a part of it is used for that purpose; the remaining part is only used as an error detection means. This novel approach allows the decoding performance to be adapted to the noise power, and provides a reduction of the computational complexity. Simulation results obtained with and without complexity optimization are presented and compared in the context of the AIS system.

This paper presents a Bayesian fusion technique for multi-band images. The observed images are related to the high spectral and high spatial resolution image to be recovered through physical degradations, e.g., spatial and spectral blurring and/or subsampling defined by the sensor characteristics. The fusion problem is formulated within a Bayesian estimation framework. An appropriate prior distribution related to the linear mixing model for hyperspectral images is introduced. To compute Bayesian estimators of the scene of interest from its posterior distribution, a Gibbs sampling algorithm is proposed to generate samples asymptotically distributed according to the target distribution. To efficiently sample from this high-dimensional distribution, a Hamiltonian Monte Carlo step is introduced in this Gibbs sampler. The efficiency of the proposed fusion method is evaluated with respect to several state-of-the-art fusion techniques.

This paper studies a new Bayesian algorithm for fusing hyperspectral and multispectral images. The observed images are related to the high spatial resolution hyperspectral image to be recovered through physical degradations, e.g., spatial and spectral blurring and/or sub-sampling defined by the sensor characteristics. In this work, we assume that the spectral response of the multispectral sensor is unknown as it may not be available in practical applications. The resulting fusion problem is formulated within a Bayesian estimation framework, which is very convenient to model the uncertainty regarding the multispectral sensor characteristics and the scene to be estimated. The high spatial resolution hyperspectral image is then inferred from its posterior distribution. More precisely, to compute the Bayesian estimators associated with this posterior, a Markov chain Monte Carlo algorithm is proposed to generate samples asymptotically distributed according to the distribution of interest. Simulation results demonstrate the efficiency of the proposed fusion method when compared with several state-of-the-art fusion techniques.

This paper addresses the problem of ultrasound image restoration within a Bayesian framework. The distribution of the ultrasound image is assumed to be a generalized Gaussian distribution (GGD). The main contribution of this work is to propose a hierarchical Bayesian model for estimating the GGD parameters. The Bayesian estimators associated with this model are difficult to be expressed in closed form. Thus we investigate a Markov chain Monte Carlo method which is used to generate samples asymptotically distributed according to the posterior of interest. These generated samples are finally used to compute the Bayesian estimators of the GGD parameters. The performance of the proposed Bayesian model is tested with synthetic data and compared with the performance obtained with the expectation maximization algorithm.

This paper introduces a new model for delay/Doppler altimetry, taking into account the effect of antenna mispointing. After defining the proposed model, the effect of the antenna mispointing on the altimetric waveform is analyzed as a function of along-track and across-track angles. Two least squares approaches are investigated for estimating the parameters associated with the proposed model. The first algorithm estimates four parameters including the across-track mispointing (which affects the echo's shape). The second algorithm uses the mispointing angles provided by the star-trackers and estimates the three remaining parameters. The proposed model and algorithms are validated via simulations conducted on both synthetic and real data.

This letter considers the problem of computing the Cramer–Rao bound for the parameters of a Markov random field. Computation of the exact bound is not feasible for most fields of interest because their likelihoods are intractable and have intractable derivatives. We show here how it is possible to formulate the computation of the bound as a statistical inference problem that can be solve approximately, but with arbitrarily high accuracy, by using a Monte Carlo method. The proposed methodology is successfully applied on the Ising and the Potts models.

The concept of delay/Doppler (DD) altimetry (DDA) has been under study since the mid-1990s, aiming at reducing the measurement noise and increasing the along-track resolution in comparison with the conventional pulse-limited altimetry. This paper introduces a new model for the mean backscattered power waveform acquired by a radar altimeter operating in synthetic aperture radar mode, as well as an associated least squares (LS) estimation algorithm. As in conventional altimetry (CA), the mean power can be expressed as the convolution of three terms: the flat surface impulse response (FSIR), the probability density function of the heights of the specular scatterers, and the time/frequency point target response of the radar. An important contribution of this paper is to derive an analytical formula for the FSIR associated with DDA. This analytical formula is obtained for a circular antenna pattern, no mispointing, no vertical speed effect, and a uniform scattering. The double convolution defining the mean echo power can then be computed numerically, resulting in a 2-D semi-analytical model called the DD map (DDM). This DDM depends on three altimetric parameters: the epoch, the sea surface wave height, and the amplitude. A multi-look model is obtained by summing all the reflected echoes from the same along-track surface location of interest after applying appropriate delay compensation (range migration) to align the DDM on the same reference. The second contribution of this paper concerns the estimation of the parameters associated with the multi-look semi-analytical model. An LS approach is investigated by means of the Levenberg-Marquardt algorithm. Simulations conducted on simulated altimetric waveforms allow the performance of the proposed estimation algorithm to be appreciated. The analysis of Cryosat-2 waveforms shows an improvement in parameter estimation when compared to the CA.

This paper presents a nonlinear mixing model for joint hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are linear combinations of known pure spectral components corrupted by an additional nonlinear term, affecting the end members and contaminated by an additive Gaussian noise. A Markov random field is considered for nonlinearity detection based on the spatial structure of the nonlinear terms. The observed image is segmented into regions where nonlinear terms, if present, share similar statistical properties. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint nonlinear unmixing and nonlinearity detection algorithm. The performance of the proposed strategy is first evaluated on synthetic data. Simulations conducted with real data show the accuracy of the proposed unmixing and nonlinearity detection strategy for the analysis of hyperspectral images.

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are post-nonlinear functions of unknown pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using second-order polynomials leading to a polynomial post-nonlinear mixing model. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding an unsupervised nonlinear unmixing algorithm. Due to the large number of parameters to be estimated, an efficient Hamiltonian Monte Carlo algorithm is investigated. The classical leapfrog steps of this algorithm are modified to handle the parameter constraints. The performance of the unmixing strategy, including convergence and parameter tuning, is first evaluated on synthetic data. Simulations conducted with real data finally show the accuracy of the proposed unmixing strategy for the analysis of hyperspectral images.

This paper studies a pixel by pixel nonlinearity detector for hyperspectral image analysis. The reflectances of linearly mixed pixels are assumed to be a linear combination of known pure spectral components (endmembers) contaminated by additive white Gaussian noise. Nonlinear mixing, however, is not restricted to any prescribed nonlinear mixing model. The mixing coefficients (abundances) satisfy the physically motivated sum-to-one and positivity constraints. The proposed detection strategy considers the distance between an observed pixel and the hyperplane spanned by the endmembers to decide whether that pixel satisfies the linear mixing model (null hypothesis) or results from a more general nonlinear mixture (alternative hypothesis). The distribution of this distance is derived under the two hypotheses. Closed-form expressions are then obtained for the probabilities of false alarm and detection as functions of the test threshold. The proposed detector is compared to another nonlinearity detector recently investigated in the literature through simulations using synthetic data. It is also applied to a real hyperspectral image.

This paper focuses on the performance of time of arrival estimators for distress beacon signals which are defined by pulses with smooth transitions. These signals are used in the satellite-based search and rescue Cospas-Sarsat system. We propose a signal model based on sigmoidal functions. Closed-form expressions for the modified Cramér-Rao bounds associated with the parameters of this model are derived. The obtained expressions are easy to interpret since they analytically depend on the system parameters. Simulations conducted on realistic search and rescue signals show good agreement with the theoretical results.

This paper presents a demodulation algorithm for automatic identification system (AIS) signals received by a satellite. The main contribution of this work is to consider the phase recovery problem for an unknown modulation index, coupled with a time-varying phase shift. The proposed method is based on a demodulator introduced in a previous paper based on a Viterbi-type algorithm applied to an extended trellis. The states of this extended trellis are composed of a trellis-code state and of a cyclic redundancy check state. The bit stuffing mechanism is taken into account by defining special conditional transitions in the extended trellis. This algorithm estimates and tracks the phase shift by modifying the Euclidean distance used in the trellis. Simulation results obtained with and without phase tracking are presented and compared in the context of the AIS system.

Multifractal analysis has matured into a widely used signal and image processing tool. Due to the statistical nature of multifractal processes (strongly non-Gaussian and intricate dependence) the accurate estimation of multifractal parameters is very challenging in situations where the sample size is small (notably including a range of biomedical applications) and currently available estimators need to be improved. To overcome such limitations, the present contribution proposes a Bayesian estimation procedure for the multifractality (or intermittence) parameter. Its originality is threefold: First, the use of wavelet leaders, a recently introduced multiresolution quantity that has been shown to yield significant benefits for multifractal analysis; Second, the construction of a simple yet generic semi-parametric model for the marginals and covariance structure of wavelet leaders for the large class of multiplicative cascade based multifractal processes; Third, the construction of original Bayesian estimators associated with the model and the constraints imposed by multifractal theory. Performance are numerically assessed and illustrated for synthetic multifractal processes for a range of multifractal parameter values. The proposed procedure yields significantly improved estimation performance for small sample sizes.

BACKGROUND: This paper introduces a new constrained model and the corresponding algorithm, called unsupervised Bayesian linear unmixing (uBLU), to identify biological signatures from high dimensional assays like gene expression microarrays. The basis for uBLU is a Bayesian model for the data samples which are represented as an additive mixture of random positive gene signatures, called factors, with random positive mixing coefficients, called factor scores, that specify the relative contribution of each signature to a specific sample. The particularity of the proposed method is that uBLU constrains the factor loadings to be non-negative and the factor scores to be probability distributions over the factors. Furthermore, it also provides estimates of the number of factors. A Gibbs sampling strategy is adopted here to generate random samples according to the posterior distribution of the factors, factor scores, and number of factors. These samples are then used to estimate all the unknown parameters. RESULTS: Firstly, the proposed uBLU method is applied to several simulated datasets with known ground truth and compared with previous factor decomposition methods, such as principal component analysis (PCA), non negative matrix factorization (NMF), Bayesian factor regression modeling (BFRM), and the gradient-based algorithm for general matrix factorization (GB-GMF). Secondly, we illustrate the application of uBLU on a real time-evolving gene expression dataset from a recent viral challenge study in which individuals have been inoculated with influenza A/H3N2/Wisconsin. We show that the uBLU method significantly outperforms the other methods on the simulated and real data sets considered here. CONCLUSIONS: The results obtained on synthetic and real data illustrate the accuracy of the proposed uBLU method when compared to other factor decomposition methods from the literature (PCA, NMF, BFRM, and GB-GMF). The uBLU method identifies an inflammatory component closely associated with clinical symptom scores collected during the study. Using a constrained model allows recovery of all the inflammatory genes in a single factor.

Much attention has been recently devoted to the analysis of coastal altimetric waveforms. When approaching the coast, altimetric waveforms are sometimes corrupted by peaks caused by high reflective areas inside the illuminated land surfaces or by the modification of the sea state close to the shoreline. This paper introduces a new parametric model for these peaky altimetric waveforms. This model assumes that the received altimetric waveform is the sum of a Brown echo and an asymmetric Gaussian peak. The asymmetric Gaussian peak is parameterized by a location, an amplitude, a width, and an asymmetry coefficient. A maximum-likelihood estimator is studied to estimate the Brown plus peak model parameters. The Cramér-Rao lower bounds of the model parameters are then derived providing minimum variances for any unbiased estimator, i.e., a reference in terms of estimation error. The performance of the proposed model and the resulting estimation strategy are evaluated via many simulations conducted on synthetic and real data. Results obtained in this paper show that the proposed model can be used to retrack efficiently standard oceanic Brown echoes as well as coastal echoes corrupted by symmetric or asymmetric Gaussian peaks. Thus, the Brown with Gaussian peak model is useful for analyzing altimetric measurements closer to the coast.

Analysis and comparison of linear and hybrid/compact dual-polarization (dual-pol) synthetic aperture radar (SAR) imagery have gained a wholly new importance in the last few years, in particular, with the advent of new spaceborne SARs such as the Japanese ALOS PALSAR, the Canadian RADARSAT-2, and the German TerraSAR-X. Compact polarimetry, hybrid dual-pol, and quad-pol modes are newly promoted in the literature for future SAR missions. In this paper, we investigate and compare different hybrid/compact and linear dual-pol modes in terms of the estimation of the degree of polarization (DoP). The DoP has long been recognized as one of the most important parameters characterizing a partially polarized electromagnetic wave. It can be effectively used to characterize the information content of SAR data. We study and compare the information content of the intensity data provided by different hybrid/compact and linear dual-pol SAR modes. For this purpose, we derive the joint distribution of multilook SAR intensity images. We use this distribution to derive the maximum likelihood and moment-based estimators of the DoP in hybrid/compact and linear dual-pol modes. We evaluate and compare the performance of these estimators for different modes on both synthetic and real data, which are acquired by RADARSAT-2 spaceborne and NASA/JPL airborne SAR systems, over various terrain types such as urban, vegetation, and ocean.

This paper studies a nonlinear mixing model for hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated by polynomials leading to a polynomial post-nonlinear mixing model. We have shown in a previous paper that the parameters involved in the resulting model can be estimated using least squares methods. A generalized likelihood ratio test based on the estimator of the nonlinearity parameter is proposed to decide whether a pixel of the image results from the commonly used linear mixing model or from a more general nonlinear mixing model. To compute the test statistic associated with the nonlinearity detection, we propose to approximate the variance of the estimated nonlinearity parameter by its constrained Cramér-Rao bound. The performance of the detection strategy is evaluated via simulations conducted on synthetic and real data. More precisely, synthetic data have been generated according to the standard linear mixing model and three nonlinear models from the literature. The real data investigated in this study are extracted from the Cuprite image, which shows that some minerals seem to be nonlinearly mixed in this image. Finally, it is interesting to note that the estimated abundance maps obtained with the post-nonlinear mixing model are in good agreement with results obtained in previous studies.

Linear spectral unmixing is a challenging problem in hyperspectral imaging that consists of decomposing an observed pixel into a linear combination of pure spectra (or endmembers) with their corresponding proportions (or abundances). Endmember extraction algorithms can be employed for recovering the spectral signatures while abundances are estimated using an inversion step. Recent works have shown that exploiting spatial dependencies between image pixels can improve spectral unmixing. Markov random fields (MRF) are classically used to model these spatial correlations and partition the image into multiple classes with homogeneous abundances. This paper proposes to define the MRF sites using similarity regions. These regions are built using a self-complementary area filter that stems from the morphological theory. This kind of filter divides the original image into flat zones where the underlying pixels have the same spectral values. Once the MRF has been clearly established, a hierarchical Bayesian algorithm is proposed to estimate the abundances, the class labels, the noise variance, and the corresponding hyperparameters. A hybrid Gibbs sampler is constructed to generate samples according to the corresponding posterior distribution of the unknown parameters and hyperparameters. Simulations conducted on synthetic and real AVIRIS data demonstrate the good performance of the algorithm.

This paper addresses the problem of estimating the Potts parameter β jointly with the unknown parameters of a Bayesian model within a Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because performing inference on β requires computing the intractable normalizing constant of the Potts model. In the proposed MCMC method, the estimation of β is conducted using a likelihood-free Metropolis-Hastings algorithm. Experimental results obtained for synthetic data show that estimating β jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of β. On the other hand, choosing an incorrect value of β can degrade estimation performance significantly. To illustrate the interest of this method, the proposed algorithm is successfully applied to real bidimensional SAR and tridimensional ultrasound images.

This paper describes a Gaussian process based method for nonlinear hyperspectral image unmixing. The proposed model assumes a nonlinear mapping from the abundance vectors to the pixel reflectances contaminated by an additive white Gaussian noise. The parameters involved in this model satisfy physical constraints that are naturally expressed within a Bayesian framework. The proposed abundance estimation procedure is applied simultaneously to all pixels of the image by maximizing an appropriate posterior distribution which does not depend on the endmembers. After determining the abundances of all image pixels, the endmembers contained in the image are estimated by using Gaussian process regression. The performance of the resulting unsupervised unmixing strategy is evaluated through simulations conducted on synthetic data.

Subspace estimation using relatively few samples is a frequently encountered problem in numerous applications, including hyperspectral imagery the target application of this paper. We address this problem in a Bayesian framework assuming that some rough prior knowledge about the subspace is available. Our approach is based on the CS decomposition of an orthogonal matrix whose columns span the subspace of interest. This parametrization only involves mild assumptions about the distribution of the angles between the actual subspace and the prior subspace, and is intuitively appealing. We derive the posterior distribution for the matrices involved in the CS decomposition and the angles between subspaces, and we propose a Gibbs sampling scheme to compute the minimum mean-square distance estimator of the subspace of interest. The estimator accuracy is evaluated through numerical simulations and tested against real hyperspectral data.

This paper studies the performance of the maximum likelihood estimators (MLE) for the parameters of multivariate generalized Gaussian distributions. When the shape parameter belongs to ]0, 1[, we have proved that the scatter matrix MLE exists and is unique up to a scalar factor. After providing some elements about this proof, an estimation algorithm based on a Newton-Raphson recursion is investigated. Some experiments illustrate the convergence speed of this algorithm. The bias and consistency of the scatter matrix estimator are then studied for different values of the shape parameter. The performance of the shape parameter estimator is finally addressed by comparing its variance to the Cramér-Rao bound.

Spectral model is simple and efficient for modeling the rain attenuation which occurs in satellite communication channels. The prediction of this attenuation series is a vital step for adaptive coding or adaptive power control, which can improve the efficiency of a communication system. In simulation tasks, the discretized spectral model is usually used for generating the attenuation sequence. Due to this reason, in this paper we derive the conditional probability distribution of the predicted attenuation based on the discretized spectral model. This predictor can be used as a bound for others linear or nonlinear predictor of this model.

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data.

This paper addresses the problem of jointly estimating the statistical distribution and segmenting lesions in multiple-tissue high-frequency skin ultrasound images. The distribution of multiple-tissue images is modeled as a spatially coherent finite mixture of heavy-tailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by enforcing local dependence between the mixture components. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a label-vector associating each voxel to a tissue. More precisely, a hybrid Metropolis-within-Gibbs sampler is used to draw samples that are asymptotically distributed according to the posterior distribution of the Bayesian model. The Bayesian estimators of the model parameters are then computed from the generated samples. Simulation results are conducted on synthetic data to illustrate the performance of the proposed estimation strategy. The method is then successfully applied to the segmentation of in vivo skin tumors in high-frequency 2-D and 3-D ultrasound images.

This paper studies a hierarchical Bayesian model for nonlinear hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are polynomial functions of linear mixtures of pure spectral components contaminated by an additive white Gaussian noise. The parameters involved in this model satisfy constraints that are naturally expressed within a Bayesian framework. A Gibbs sampler allows one to sample the unknown abundances and nonlinearity parameters according to the joint posterior of interest. The performance of the resulting unmixing strategy is evaluated thanks to simulations conducted on synthetic and real data.

This paper investigates a Bayesian model and a Markov chain Monte Carlo (MCMC) algorithm for gene factor analysis. Each sample in the dataset is decomposed as a linear combination of characteristic gene signatures (also referred to as factors) following a linear mixing model. To enforce the sparsity of the relative contribution (called factor score) of each gene signature to a specific sample, constrained Bernoulli-Gaussian distributions are elected as prior distributions for these factor scores. This distribution allows one to ensure non-negativity and full-additivity constraints for the scores that are interpreted as concentrations. The complexity of the resulting Bayesian estimators is alleviated by using a Gibbs sampler which generates samples distributed according to the posterior distribution of interest. These samples are then used to approximate the standard maximum a posteriori (MAP) or minimum mean square error (MMSE) estimators. The accuracy of the proposed Bayesian method is illustrated by simulations conducted on synthetic and real data.

This paper studies a variational Bayesian unmixing algorithm for hyperspectral images based on the standard linear mixing model. Each pixel of the image is modeled as a linear combination of endmembers whose corresponding fractions or abundances are estimated by a Bayesian algorithm. This approach requires to define prior distributions for the parameters of interest and the related hyperparameters. After defining appropriate priors for the abundances (uniform priors on the interval (0,1)), the joint posterior distribution of the model parameters and hyperparameters is derived. The complexity of this distribution is handled by using variational methods that allow the joint distribution of the unknown parameters and hyperparameter to be approximated. Simulation results conducted on synthetic and real data show similar performances than those obtained with a previously published unmixing algorithm based on Markov chain Monte Carlo methods, with a significantly reduced computational cost.

The delineation of P and T waves is important for the interpretation of ECG signals. We propose a Bayesian detection-estimation algorithm for simultaneous detection, delineation, and estimation of P and T waves. A block Gibbs sampler exploits the strong local dependencies in ECG signals by imposing block constraints on the P and T wave locations. The proposed algorithm is evaluated on the annotated QT database and compared with two classical algorithms.

Like its linear counterpart, the Kernel Least Mean Square (KLMS) algorithm is also becoming popular in nonlinear adaptive filtering due to its simplicity and robustness. The "kernelization" of the linear adaptive filters modifies the statistics of the input signals, which now depends on the parameters of the used kernel. A Gaussian KLMS has two design parameters; the step size and the kernel bandwidth. Thus, new analytical models are required to predict the kernel-based algorithm behavior as a function of the design parameters. This pa per studies the stochastic behavior of the Gaussian KLMS algorithm for white Gaussian input signals. The resulting model accurately predicts the algorithm behavior and can be used for choosing the algorithm parameters in order to achieve a prescribed performance.

This paper addresses the problem of estimating the statistical distribution of multiple-tissue non-stationary ultrasound images of skin. The distribution of multiple-tissue images is modeled as a finite mixture of Heavy-Tailed Rayleigh distributions. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then derived to jointly estimate the mixture parameters and a label vector associating each voxel to a tissue. Precisely, a hybrid Metropolis-within-Gibbs sampler is proposed to draw samples that are asymptotically distributed according to the posterior distribution of the Bayesian model. These samples are then used to compute the Bayesian estimators of the model parameters. Simulation results are conducted on synthetic data to illustrate the performance of the proposed estimation strategy. The method is then successfully applied to the detection of an in-vivo skin lesion in a high frequency 3D ultrasound image.

This paper studies a linear radial basis function network (RBFN) for unmixing hyperspectral images. The proposed RBFN assumes that the observed pixel reflectances are nonlinear mixtures of known end members (extracted from a spectral library or estimated with an end member extraction algorithm), with unknown proportions (usually referred to as abundances). We propose to estimate the model abundances using a linear combination of radial basis functions whose weights are estimated using training samples. The main contribution of this paper is to study an orthogonal least squares algorithm which allows the number of RBFN centers involved in the abundance estimation to be significantly reduced. The resulting abundance estimator is combined with a fully constrained estimation procedure ensuring positivity and sum-to-one constraints for the abundances. The performance of the nonlinear unmixing strategy is evaluated with simulations conducted on synthetic and real data.

This paper studies estimation algorithms for nonlinear hyperspectral image unmixing. The proposed unmixing model assumes that the pixel reflectances are polynomial functions of linear mixtures of pure spectral components contaminated by an additive white Gaussian noise. A hierarchical Bayesian algorithm and an optimization method are proposed for solving the resulting unmixing problem. The parameters involved in the proposed model satisfy constraints that are naturally included in the estimation procedure. The performance of the unmixing strategies is evaluated thanks to simulations conducted on synthetic and real data.

This paper studies the potential interest of the multivariate Pearson system for the statistical modeling of images acquired by different sensors. These images include optical and synthetic aperture radar (SAR) remote sensing images. The univariate Pearson system has shown good capacities to capture the statistical properties of SAR images. This paper introduces a generalization of this system to multidimensional vectors with a particular attention to the bivariate case. The method of moments is investigated to estimate the unknown parameters of bivariate Pearson distributions. The estimation performance is evaluated using synthetic and real data.

Nonlinear models have recently shown interesting properties for spectral unmixing. This paper considers a generalized bilinear model recently introduced for unmixing hyperspectral images. Different algorithms are studied to estimate the parameters of this bilinear model. The positivity and sum-to-one constraints for the abundances are ensured by the proposed algorithms. The performance of the resulting unmixing strategy is evaluated via simulations conducted on synthetic and real data.

Coastal altimetric waveforms may be corrupted by peaks. A simple parametric model was recently introduced to model peaky altimetric waveforms. This model assumes that the received altimetric waveform is the sum of a Brown echo and a Gaussian peak. This model has provided interesting results for symmetric peaks affecting altimetric signals. However, it is not appropriate for altimetric signals corrupted by asymmetric peaks. This paper introduces a Brown with asymmetric Gaussian peak model for altimetric waveforms. The parameters of this model are estimated by a maximum likelihood estimator. The performance of the proposed model and the resulting estimation strategy is evaluated via simulations con ducted on synthetic and real data.

Synthetic Aperture Radar (SAR) is a powerful tool strongly employed in maritime monitoring and surveillance. Among different polarimetric SAR modes, dual-pol SAR data are widely used for monitoring large ocean and coastal areas. The degree of polarization (DoP) is a fundamental quantity characterizing a partially polarized electromagnetic field. The performance of the DoP is studied for ship detection under different polarizations in hybrid/compact and linear dual-pol SAR imagery. Experiments are performed on C-band polarimetric data acquired by RADARSAT-2 over San Francisco Bay and the Strait of Gibraltar.

This paper describes a new algorithm for hyperspectral image unmixing. Most unmixing algorithms proposed in the literature do not take into account the possible spatial correlations between the pixels. In this paper, a Bayesian model is introduced to exploit these correlations. The image to be unmixed is assumed to be partitioned into regions (or classes) where the statistical properties of the abundance coefficients are homogeneous. A Markov random field, is then proposed to model the spatial dependencies between the pixels within any class. Conditionally upon a given class, each pixel is modeled by using the classical linear mixing model with additive white Gaussian noise. For this model, the posterior distributions of the unknown parameters and hyperparameters allow the parameters of interest to be inferred. These parameters include the abundances for each pixel, the means and variances of the abundances for each class, as well as a classification map indicating the classes of all pixels in the image. To overcome the complexity of the posterior distribution, we consider a Markov chain Monte Carlo method that generates samples asymptotically distributed according to the posterior. The generated samples are then used for parameter and hyperparameter estimation. The accuracy of the proposed algorithms is illustrated on synthetic and real data.

Nonlinear models have recently shown interesting properties for spectral unmixing. This paper studies a generalized bilinear model and a hierarchical Bayesian algorithm for unmixing hyperspectral images. The proposed model is a generalization not only of the accepted linear mixing model but also of a bilinear model that has been recently introduced in the literature. Appropriate priors are chosen for its parameters to satisfy the positivity and sum-to-one constraints for the abundances. The joint posterior distribution of the unknown parameter vector is then derived. Unfortunately, this posterior is too complex to obtain analytical expressions of the standard Bayesian estimators. As a consequence, a Metropolis-within-Gibbs algorithm is proposed, which allows samples distributed according to this posterior to be generated and to estimate the unknown model parameters. The performance of the resulting unmixing strategy is evaluated via simulations conducted on synthetic and real data.

This paper addresses the issue of cartographic database (DB) creation or updating using high-resolution synthetic aperture radar and optical images. In cartographic applications, objects of interest are mainly buildings and roads. This paper proposes a processing chain to create or update building DBs. The approach is composed of two steps. First, if a DB is available, the presence of each DB object is checked in the images. Then, we verify if objects coming from an image segmentation should be included in the DB. To do those two steps, relevant features are extracted from images in the neighborhood of the considered object. The object removal/inclusion in the DB is based on a score obtained by the fusion of features in the framework of Dempster-Shafer evidence theory.

In this paper, we address the problem of unmixing hyperspectral images in a semi-supervised framework using the normal compositional model recently introduced by Eismann and Stein. Each pixel of the image is modeled as a linear combination of random endmembers. More precisely, endmembers are modeled as Gaussian vectors whose means belong to a known spectral library. This paper proposes to estimate the number of endmembers involved in the mixture, as well as the mixture coefficients (referred to as abundances) using a trans-dimensional algorithm. Appropriate prior distributions are assigned to the abundance vector (to satisfy constraints inherent to hyperspectral imagery), the noise variance and the number of components involved in the mixture model. The computational complexity of the resulting posterior distribution is alleviated by constructing an hybrid Gibbs algorithm which generates samples distributed according to this posterior distribution. As the number of endmembers is unknown, the sampler has to jump between spaces of different dimensions. This is achieved by a reversible jump Markov chain Monte Carlo method that allows one to handle the model order selection problem. The performance of the proposed methodology is evaluated thanks to simulations conducted on synthetic data.

We consider Bayesian detection/classification of discrete random parameters that are strongly dependent locally due to some deterministic local constraint. Based on the recently introduced partially collapsed Gibbs sampler (PCGS) principle, we develop a Markov chain Monte Carlo method that tolerates and even exploits the challenging probabilistic structure imposed by deterministic local constraints. We study the application of our method to the practically relevant case of nonuniformly spaced binary pulses with a known minimum distance. Simulation results demonstrate significant performance gains of our method compared to a recently proposed PCGS that is not specifically designed for the local constraint.

Information contained in polarimetric images can be characterized by a scalar parameter called the polarization degree. This parameter is usually estimated using four polarimetric images. However, acquisition and registration of four images are complex and costly. Thus, reducing the number of required images can be of great interest for practical applications. In coherent illumination, these images are degraded by speckle noise. This noise can be reduced by transforming the original single-look images into multi-look images. We provide maximum likelihood estimators of the polarization degree in the general case of multi-look intensity images. The estimators are derived based on only two measurements, under coherent illumination and fully developed speckle. We evaluate our method on synthetic data and compare its performance with that of moment-based methods.

Analysis of dual-polarized SAR imagery has gained new importance with the recent launches of ALOS PALSAR, RADARSAT-2, and TerraSAR-X polarimetric SAR systems. Information contained in polarimetric images, collected by these SAR systems, can be characterized by a scalar parameter called the degree of polarization. This parameter has long been recognized as one of the most important parameters characterizing a partially polarized electromagnetic wave. In this paper, we provide maximum likelihood and moment-based estimators of the degree of polarization in dual-polarized SAR imagery. We evaluate and compare the performance of these estimators on RADARSAT-2 polarimetric data, over various terrain types such as urban, vegetation, and ocean.

This paper studies database updating using optical and synthetic aperture radar images. Logistic regression is used to model the conditional probability of presence/absence of buildings given features extracted from the images. The logistic regression parameters are estimated using the maximum likelihood method. Binary hypothesis tests are then constructed from these estimates to detect changes between the optical/radar images and the existing database. The estimation and detection algorithms are evaluated using simulated and real data sets.

This paper addresses the issue of cartographic database creation or updating using high resolution SAR and optical images. It proposes a processing chain to create or update road databases in urban environment. The approach is composed of two steps. First, if a database is available, the presence of each database object is checked in the images. Then, we verify if road hypotheses extracted from images should be included in the database. These two steps are conducted by extracting relevant features from the images in the neighborhood of the considered object. The object removal/inclusion in the database is based on a score obtained by the fusion of features in the framework of Dempster-Shafer evidence theory.

The degree of polarization (DoP) has long been recognized as one of the most important parameters characterizing partially polarized electromagnetic waves. This parameter can be effectively used to describe the information content of polarimetric images collected by synthetic aperture radar (SAR) systems. Estimation of DoP is standardly performed using four measurements. In SAR compact polarimetry (CP), however, only two measurements are available. In this paper, we develop maximum likelihood estimators of the DoP, in SAR CP modes, based on only two intensity images. We evaluate and compare the performance of these estimators for different CP modes on RADARSAT-2 polarimetric data, over various terrain types such as urban, vegetation, and ocean.

This paper addresses the problem of classifying altimetric signals according to their shapes. The proposed classifier is divided into three steps. A one-class support vector machine method is first used to isolate the large amount of Brown-like echoes from others signals which are considered as outliers. The second step extracts pertinent features from the the remaining echoes (which cannot be well described by the Brown model). These features are projected onto discriminant axes using linear discriminant analysis. The final step classifies the projected feature vectors using a standard Bayesian classifier. The proposed three step classification strategy is evaluated on supervised real altimetric echoes.

Choosing the appropriate parameter prior distributions associated to a given bayesian model is a challenging problem. Conjugate priors can be selected for simplicity motivations. However, conjugate priors can be too restrictive to accurately model the available prior information. This paper studies a new generative supervised classifier which assumes that the parameter prior distributions conditioned on each class are mixtures of Dirichlet processes. The motivations for using mixtures of Dirichlet processes is their known ability to model accurately a large class of probability distributions. A Monte Carlo method allowing one to sample according to the resulting class-conditional posterior distributions is then studied. The parameters appearing in the class-conditional densities can then be estimated using these generated samples (following bayesian learning). The proposed supervised classifier is applied to the classification of altimetric waveforms backscattered from different surfaces (oceans, ices, forests, and deserts). This classification is a first step before developing tools allowing for the extraction of useful geophysical information from altimetric waveforms backscattered from nonoceanic surfaces.

This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of so-called endmembers. These endmembers are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model endmembers as Gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous N-finder (N-FINDR) or Vertex Component Analysis (VCA) algorithms. This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters. A hybrid Gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances. The performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images.

In this paper, we propose a Bayesian model and a Monte Carlo Markov chain (MCMC) algorithm for reconstructing images that consist of only few non-zero pixels. An appropriate distribution that promotes sparsity is proposed as prior distribution for the pixel values. The hyperparameters involved in the modeling are also assigned prior distributions, resulting in a hierarchical model. A Gibbs sampler allows us to draw samples distributed according the full posterior of interest. These samples are then used to approximate standard maximum a posteriori (MAP) estimator. By conducting some simulations, we show that the proposed estimator clearly outperforms previous estimators proposed in the literature.

In this paper, a data-driven extension of the variational algorithm is proposed. Based on a few selected sensors, target tracking is performed distributively without any information about the observation model. Tracking under such conditions is possible if one exploits the information collected from extra inter-sensor RSSI measurements. The target tracking problem is formulated as a kernel matrix completion problem. A probabilistic kernel regression is then proposed that yields a Gaussian likelihood function. The likelihood is used to derive an efficient and accelerated version of the variational filter without resorting to Monte Carlo integration. The proposed data-driven algorithm is, by construction, robust to observation model deviations and adapted to non-stationary environments.

This paper addresses the issue of cartographic database creation or update using high resolution SAR and optical images. In cartographic applications, objects of interest are mainly buildings and roads. This paper proposes a processing chain to update building databases. The approach is composed of two steps. First, the presence of each database object is checked in the images. Then, we verify if objects coming from an image segmentation should be added in the database. To do those two steps, features are extracted from images in the neighborhood of the considered object. The object removal/inclusion in the database is based on a score obtained by the fusion of features in the framework of Dempster Shafer evidence theory.

This paper addresses the problem of defining a similarity measure between an observed Gaussian image and a binary image constructed from a cartographic database. The main idea is to assume that the binary image has been obtained by thresholding an unobserved Gaussian image correlated with the observed image. The proposed statistical model is then used to estimate its unknown parameters using the maximum likelihood method. The paper discusses a possible application to change detection between a cartographic vector data base and an optical image.

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.

This paper studies the statistical behavior of an affine combination of the outputs of two LMS adaptive filters that simultaneously adapt using the same white Gaussian input. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square error (MSE). The linear combination studied is a generalization of the convex combination, in which the combination factor is restricted to the interval (0,1). The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the MSE. The optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then, a new scheme is proposed for practical applications. It is shown that the practical scheme yields close-to-optimal performance when properly designed (as suggested by the theoretical optimal).

A new family of distributions, constructed by summing two correlated gamma random variables, is studied. First, a simple closed form expression for their density is derived. Second, the three parameters characterizing such a density are estimated by using the maximum likelihood (ML) principle. Numerical simulations are conducted to compare the performance of the ML estimator against those of the conventional estimator of moments. Finally, a multiresolution multivariate gamma based modeling of Internet traffic illustrates the potential interest of the proposed distributions for the detection of anomalies. Aggregated times series of IP packet counts are split into adjacent non overlapping time blocks. The distribution of the resulting time series are modeled by the proposed multivariate gamma based distributions, over a collection of different aggregation levels. The anomaly detection strategy is based on tracking changes along time of the corresponding multiresolution parameters.

This paper addresses the problem of unmixing hyperspectral images contamined by additive colored noise. Each pixel of the image is modeled as a linear combination of pure materials (denoted as end-members) corrupted by an additive zero mean Gaussian noise sequence with unknown covariance matrix. Appropriate priors are defined ensuring positivity and additivity constraints on the mixture coefficients (denoted as abundances). These coefficients as well as the noise covariance matrix are then estimated from their joint posterior distribution. A Gibbs sampling strategy generates abundances and noise covariance matrices distributed according to the joint posterior. These samples are then averaged for minimum mean square error estimation.

This paper studies a Bayesian classifier which recognizes Gaussian minimum shift keying (GMSK) modulated signals with different bandwiths. We focus on identifying two different GMSK signals with BT = 0.25 and BT = 0.5 standardized by the consultative committee for space data system (CCSDS) for future space missions. The main idea of the proposed classifier is to compute the posterior probability of the observation sequence given each possible model by a modified Baum-Welch (BW) algorithm. The received GMSK signals are then classified according to the maximum a posteriori (MAP) rule.

This paper studies a Bayesian algorithm for estimating the parameters associated to Brown's model. The joint posterior distribution of the unknown parameter vector (amplitude, epoch and significant wave height) associated with this model is derived. This posterior is too complex to obtain closed form expressions of the minimum mean square error and the maximumaposterioriestimators. We propose to sample according to this distribution using an hybrid Metropolis within Gibbs algorithm. The simulated samples are then used to estimate the unknown parameters of Brown's model. The proposed strategy provides better estimations than the standard maximum likelihood estimator at the price of an increased computational cost.

This paper addresses the problem of classifying altimetric waveforms backscattered from different kinds of surfaces including oceans, ices, deserts and forests. Appropriate features associated with altimetric radar waveforms are first introduced for this classification. These features are completed by radiometer temperatures and pre-processed using a linear discriminant analysis for dimensionality reduction. The classification of altimetric waveforms is finally achieved using the resulting pre-processed vector with reduced dimension. Different classification strategies are finally considered. These strategies are based on the nearest mean rule, the nearest neighbor method or on the multilayer perceptron. Various simulation results illustrate the performance of the proposed classifier.

The adaptive coherence estimator (ACE) is known to be the generalized likelihood ratio test (GLRT) in partially homogeneous environments, i.e., when the covariance matrix Msof the secondary data is proportional to the covariance matrix Mpof the vector under test (or Ms= gamma/Mp). In this letter, we show that ACE is indeed the GLRT for a broader class of nonhomogeneous environments, more precisely when Msis a random matrix, with inverse complex Wishart prior distribution whose mean only is proportional to Mp. Furthermore, we prove that, for this class of heterogeneous environments, the ACE detector satisfies the constant false alarm rate (CFAR) property with respect to gamma and Mp.

This paper studies a family of distributions constructed from multivariate gamma distributions to model the statistical properties of multisensor synthetic aperture radar (SAR) images. These distributions referred to as multisensor multivariate gamma distributions (MuMGDs) are potentially interesting for detecting changes in SAR images acquired by different sensors having different numbers of looks. The first part of this paper compares different estimators for the parameters of MuMGDs. These estimators are based on the maximum likelihood principle, the method of inference function for margins, and the method of moments. The second part of the paper studies change detection algorithms based on the estimated correlation coefficient of MuMGDs. Simulation results conducted on synthetic and real data illustrate the performance of these change detectors.

This paper studies the behavior of the LMS algorithm for a special system identification problem when partial wavelet transformations restrict the algorithm's input vector to a subspace of the unknown system's input vector space. It is shown that the independence theory is not applicable in this case. A new theoretical model for the weight mean and fluctuation behaviors is developed which incorporates the correlation between successive data vectors (as opposed to using the independence theory model). Comparison of the new model predictions with Monte Carlo simulations shows good-to-excellent agreement, certainly much better than predicted by the independence theory model.

In many applications, it is required to detect, from a primary vector, the presence of a signal of interest embedded in noise with unknown statistics. We consider a situation where the training samples used to infer the noise statistics do not share the same covariance matrix as the vector under test. A Bayesian model is proposed where the covariance matrices of the primary and the secondary data are assumed to be random, with some appropriate joint distribution. The prior distributions of these matrices reflect a rough knowledge about the environment. Within this framework, the minimum mean-square error (MMSE) estimator and the maximum a posteriori (MAP) estimator of the primary data covariance matrix are derived. A Gibbs sampling strategy is presented for the implementation of the MMSE estimator. Numerical simulations illustrate the performances of these estimators and compare them with those of the sample covariance matrix estimator.

This paper addresses the problem of estimating the parameters of a family of bivariate gamma distributions whose margins have different shape parameters. These distributions are interesting to detect changes in two synthetic radar aperture (SAR) images acquired by different sensors and having different numbers of looks. The estimators based on the maximum likelihood method and the method of moments are studied for these distributions. An application to change detection is finally discussed.

This paper addresses the problem of hyperspectral image unmixing. A new hierarchical Bayesian algorithm is proposed to estimate the coefficients of a linear mixture of spectra associated to a given pixel of the image. Appropriate priors are introduced to guaranty the positivity and additivity constraints inherent to the mixture coefficients. These coefficients referred to as abundances are then estimated from their posterior following the principles of Bayesian inference. The estimation is performed by using a Gibbs sampling strategy which generates samples distributed according the abundance posterior distribution. These samples are then averaged yielding the abundance minimum mean square error estimator.

In urban areas, multipath (MP) is one of the main error sources when tracking signals used in global navigation satellite systems. The received signals subjected to MP are the sum of several delayed replicas leading to biased estimations. This paper studies a sequential Monte Carlo (SMC) algorithm which mitigates MP effects. The proposed algorithm is based on a state-space model associated to a multicorrelator GPS receiver and on a Rao Blackwellized technique which allows to achieve good performance.

We address the problem of detecting a signal of interest in the presence of noise with unknown covariance matrix, using a set of training samples. We consider a situation where the environment is not homogeneous, i.e., when the covariance matrices of the primary and the secondary data are different. A knowledge-aided Bayesian framework is proposed, where these covariance matrices are considered as random, and some information about the covariance matrix of the training samples is available. Within this framework, the maximum a priori (MAP) estimate of the primary data covariance matrix is derived. It is shown that it amounts to colored loading of the sample covariance matrix of the secondary data. The MAP estimate is in turn used to yield a Bayesian version of the adaptive matched filter. Numerical simulations illustrate the performance of this detector, and compare it with the conventional adaptive matched filter

This paper evaluates the potential interest of using bivariate gamma distributions for image registration and change detection. The first part of this paper studies estimators for the parameters of bivariate gamma distributions based on the maximum likelihood principle and the method of moments. The performance of both methods are compared in terms of estimated mean square errors and theoretical asymptotic variances. The mutual information is a classical similarity measure which can be used for image registration or change detection. The second part of the paper studies some properties of the mutual information for bivariate Gamma distributions. Image registration and change detection techniques based on bivariate gamma distributions are finally investigated. Simulation results conducted on synthetic and real data are very encouraging. Bivariate gamma distributions are good candidates allowing us to develop new image registration algorithms and new change detectors.

Echo cancellers are in wide use in both electrical (four wire to two wire mismatch) and acoustic (speaker-microphone coupling) applications. One of the main design problems is the control logic for adaptation. Basically, the algorithm weights should be frozen in the presence of double-talk and adapt quickly in the absence of double-talk. The control logic can be quite complicated (C. Breining et al., 1999) since it is often not easy to discriminate between the echo signal and the near end-speaker. This paper derives a log likelihood ratio test for deciding between double-talk (freeze weights) and a channel change (adapt quickly) using a stationary Gaussian stochastic input signal model. The probability density function of a sufficient statistic under each hypothesis is obtained and the performance of the test is evaluated as a function of the system parameters. The receiver operating characteristics indicate that it is difficult to correctly decide between double-talk and a channel change based upon a single look. However, post-detection integration of approximately one hundred sufficient statistic samples yields a detection probability close to unity with a small false alarm probability

Estimating the parameters of multivariate distributions whose densities or masses cannot be expressed in tractable closed-form is a challenging problem. This paper concentrates on a family of such discrete distributions referred to as multivariate mixed Poisson distributions (MMPDs). These distributions are interesting for modeling correlations between adjacent pixels of active and astronomical images. Several estimators of MMPD parameters are investigated. These estimators include a composite likelihood estimator and a non-linear least squares estimator

We propose a joint segmentation algorithm for piecewise constant AR processes recorded by several independent sensors. The algorithm is based on a hierarchical Bayesian model. Appropriate priors allow to introduce correlations between the change locations of the observed signals. Numerical problems inherent to Bayesian inference are solved by a Gibbs sampling strategy. The proposed joint segmentation methodology provides interesting results compared to a signal-by-signal segmentation

Subband decomposition has been shown to be a useful tool for spectral estimation, in particular when parametric methods have to be considered. Indeed, the loss of observed samples due to decimation can be compensated by the use of a suitable model, if available. This paper studies a subband multichannel autoregressive spectral estimation (SMASE) method. The proposed method decomposes the observed signal through an appropriate filter bank and processes the decimated signals by means of a multichannel autoregressive (AR) model. This model takes advantage of known correlations between different subband signals. This a priori knowledge allows to improve spectral estimation performance. Simulation results illustrate the interest of the proposed methodology for signals with continuous spectra and for sinusoids.

Multipaths cause major impairments to navigation with the Global Positioning System (GPS). Indeed, non-line-of-sight (NLOS) propagation is well known to bias GPS position estimates. A recent methodology has been proposed to overcome this limitation by estimating simultaneously the kinematic states and the multipath biases all along the observation interval. However, multipaths clearly occur relatively infrequently during time intervals of fixed duration. The paper studies a particle filtering algorithm for joint detection and estimation of multipath biases. A Rao-Blackwellized approach allows estimation of the kinematic states by extended Kalman filters, whereas multipath detection is achieved by an appropriate fixed lag particle filter.

This paper addresses abrupt change detection in multiplicative noise using the continuous wavelet transform. An optimal wavelet, maximizing a well-chosen time-scale contrast criterion is derived. The analytical optimization gives the optimal wavelet closed expression. The influence of the mother wavelet on signature-based detector performance is then demonstrated. Detection performance is characterized using receiver operating characteristic curves computed from Monte-Carlo simulations. The optimal wavelet obviously improves performance with respect to other wavelets classically used for singularity detection.

This paper studies a measure of detection performance for testing binary hypotheses by using discrete test statistics. This measure is the area under the receiver operating characteristics. This theory is applied to the detection of changes in low-flux images with the Neyman Pearson detector. An approximation of this measure can be derived. It allows to define a specific signal to noise ratio for the low-flux detector.

The localization performance of a navigation system can be improved by coupling different types of sensors. The paper focuses on INS-GPS integration. INS and GPS measurements allow a non-linear state space model, which is appropriate to particle filtering, to be defined. This model being conditionally linear Gaussian, a Rao-Blackwellization procedure can be applied to reduce the variance of the estimates.

Singular random signals are collections of singular random variables indexed over time. Singular random variables have continuous distribution with derivatives equal to zero almost everywhere. Such random variables do not seem interesting in signal processing. On the contrary, the paper shows that simple signals can be singular. This is especially the case of ARMA signals generated from discrete white noise with poles located inside a so-called singularity circle. The origin of singularity and its relations to a fractal structure are presented along with various simulations illustrating the theoretical results.

The paper addresses the important problem of signal segmentation, when signals are corrupted by multiplicative noise. A hierarchical Bayesian analysis is proposed to estimate the change-point locations and amplitudes. However, closed form expressions of the change-point parameter estimators are difficult to obtain. The proposed methodology draws samples distributed according to the change-point parameter posteriors by a metropolis-within-Gibbs algorithm. The main advantage of the algorithm is that it allows joint estimation of the parameters and hyperparameters of the hierarchical model.

We propose sliding-window multiedge detectors and reflectivity estimators for complex SAR images. The novel detectors and estimators allow to take into account additive observation noise and colored signal (speckle) and noise processes; furthermore, they employ an exponential data weighting to improve spatial resolution. In the multiedge case, simulation results demonstrate a substantial performance improvement over existing methods when the speckle is colored and additive noise is present.

This paper addresses the problem of estimating abrupt changes in synthetic aperture radar (SAR) images. The problem is formulated as a Bayesian estimation problem. Appropriate priors allow to take into account the correlations between images recorded at different dates. Unfortunately, the posterior distribution of the unknown parameters cannot be expressed in closed-form. The proposed Bayesian implementation consists of generating samples distributed according this posterior by using MCMC methods. These samples are then used to estimate various interesting features including the posterior changepoint probabilities and the posterior changepoint number. Simulations on synthetic data illustrate the proposed methodology.

This paper addresses the problem of classifying chirp signals using hierarchical Bayesian learning combined with Markov Chain Monte Carlo (MCMC) methods. Bayesian learning consists of estimating the distribution of observed data conditional upon each class from a set of training samples. Unfortunately, this estimation often requires to evaluate intractable multidimensional integrals. This paper studies an original implementation of hierarchical Bayesian learning which estimates the class conditional probability densities using MCMC methods. The performance of this implementation is compared to other existing approaches for the classification of chirp signals.

This paper addresses the problem of SAR image segmentation by using reversible jump MCMC sampling. The SAR image segmentation problem is formulated as a Bayesian estimation problem. The reversible jump MCMC algorithm is then used to generate samples distributed according to the joint posterior distribution of the unknown parameters. These samples allow to compute marginal maximum a posteriori estimates for the interesting features. The performance of the proposed methodology is illustrated via several simulation results.

The paper addresses the problem of detecting changes in the parameters of multivariate Poisson sequences. The Neyman Pearson Detector (NPD) and the, Generalized Likelihood Ratio Detector (GLRD) are easily derived for iid Poisson sequences. Unfortunately, the problem is more' complicated for correlated Poisson sequences. This paper studies the performance of the detectors obtained under the iid assumption, when the observed data are distributed according to multivariate correlated Poisson sequences. Theoretical expressions of the receiver operating characteristics are derived when the change location is known. These curves provide a reference to which other detectors can be compared. The more realistic situation of an unknown change location is finally considered.

In adaptive signal processing the principle of exponentially weighted recursive least-squares plays a major role in developing various estimation algorithms. It is based on the concept of discounting of old measurements and allows for better performance in problems with time-varying signals and signals in nonstationary noise. We show how this concept can be combined with the Bayesian methodology. We propose that the discounting of old measurements within the Bayesian framework be implemented by employing particle filters. The main idea is presented by way of a simple example. The methodology is very attractive and can be used in a very wide range of scenarios including ones that involve highly nonlinear models and non-Gaussian noise.

This paper addresses the problem of classification of digital modulations. The proposed solution uses the Bayes classifier, which is implemented by the Markov chain Monte Carlo scheme. The implementation considers classifications in the presence of phase and frequency offsets as well as residual filtering effects coming from imperfect channel equalization. The proposed approach has been tested for many scenarios and its performance has been compared with the maximum likelihood classifier and the 4/sup th/ order cumulant-based method. The obtained results show that our classifier outperforms the other methods considerably.

The paper proposes a method for on-line model selection of nonstationary time series. The method is based on computation of the covariance matrix of the data, transformation of the matrix by Housholder's tridiagonalization, and application of a clustering algorithm that can separate the Gerschgorin disks of the transformed covariance matrix into disks that correspond to the signals and noise, respectively. The method is applied to on-line estimation of the the number of harmonic signals in noise. Simulation results are presented that show the performance of the proposed method.

This paper addresses the problem of supervised classification using general Bayesian learning. General Bayesian learning consists of estimating the unknown class-conditional densities from a set of labelled samples. However, the estimation requires to evaluate intractable multidimensional integrals. This paper studies an implementation of general Bayesian learning based on Markov chain Monte Carlo (MCMC) methods.

The paper addresses the problem of determining the Cramer-Rao lower bounds for noise and abrupt change parameters, for steplike signals corrupted by multiplicative and/or additive noise. Closed-form expressions are derived for an ideal step with a known changepoint. For an unknown changepoint, the noise-free signal is modeled by a sigmoidal function parametrized by location and step rise parameters. The noise and step change CRLBs are then shown to be well approximated by the more tractable expressions derived for a known changepoint.

This paper addresses the problem of estimating sinusoidal frequencies in additive and multiplicative colored noises. Specific Yule-Walker equations yield second-order statistic-based estimates. The frequency estimates are shown to be asymptotically normally distributed. Their asymptotic covariance is derived.

We present an algorithm for the detection of extra-solar planets by occultation on the satellite COROT. Under a high flux assumption, the signal is modeled as an autoregressive process having equal mean and variance. A transit of a planet in front of a star will produce an abrupt jump in the mean/variance of the process. The Neyman-Pearson detector is derived when the abrupt change parameters are known. The theoretical distribution of the test statistic is obtained allowing the computation of the ROC curves. The generalized likelihood ratio detector is then studied for the practical case were the change parameters are unknown. This detector requires the maximum likelihood estimates of the parameters. ROC curves are then determined using computer simulations.

The paper addresses the problem of detecting two spectrally equivalent parametric processes (SEPP): the noisy AR process and the ARMA process. Higher-order statistics (HOS) are shown to be effective for detection. Two HOS based detectors are derived and compared. The fist detector studies the singularity of a HOS-based Yule-Walker matrix. The second detector filters the data by an AR filter estimated from the data; the residual HOS are then shown to be effective for the SEPP detection problem.

A large class of nonlinear phenomena can be described using bilinear systems. Such systems are very attractive since they usually require few parameters, to approximate most nonlinearities (compared to other systems). This paper addresses the problems of bilinear system identicalness using Bayesian inference. The Gibbs sampler is used to estimate the bilinear system parameters, from measurements of the system input and output signals.

The paper addresses the estimation of abrupt changes which are contaminated by multiplicative Gaussian noise. The marginal mean a posteriori or marginal maximum a posteriori estimators can be derived for estimating the position of a single abrupt change. However, these estimators have optimization or integration problems for multiple abrupt changes. The paper solves these optimization problems by using Markov chain Monte Carlo methods (MCMC).

This article tackles the problem of a Gaussian band-limited continuous signal with unknown characteristics sampled with jitter. Under this weak assumption, we demonstrate a relation linking the power spectral density of the continuous signal to the second and fourth order statistics of the measured samples. A fundamental point is that this relation does not require a knowledge of the jitter characteristics. This result can be exploited for the derivation of spectral estimation algorithms when the jitter is unknown or jitter detection tests when the sampled signal is unknown. A simulation of spectral estimation confirms the validity of the result.

The problem addressed in the paper is the detection of abrupt changes embedded in multiplicative colored Gaussian noise. The multiplicative noise is modeled by an AR process. The Neyman Pearson detector is developed when the abrupt change and noise parameters are known. This detector constitutes a reference to which suboptimal detectors can be compared. In practical applications, the abrupt change and noise parameters have to be estimated. The maximum likelihood estimator for these parameters is then derived. This allows to study the generalized likelihood ratio detector.

This paper addresses the problem of additive and multiplicative abrupt jump detection. Two detection algorithms based on the continuous wavelet transform are studied. Additive and multiplicative jumps are compared in the time-scale plane. Considering non-zero mean signals, we show that the same wavelet based algorithms can be used for the detection of additive and multiplicative jumps. However, an analysis of the variance in the time-scale plane allows us to distinguish these two kinds of jump.

Being linked by non-linear relations, the AR parameters and reflection coefficients cannot both be Gaussian. However, a statistical study can show that these two sets of parameters are Gaussian asymptotically. The aim of this paper is to show that the convergence rate of the reflection coefficient distribution to the Gaussian one depends on the position of the AR model poles in the unit circle. An analysis of the reflection coefficient Taylor expansion around the AR parameters is proposed to determine this convergence rate.